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<title>Review Exercises and Sample Exam</title>
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<div class="section end-of-chapter" id="fwk-redden-ch02_s08" version="5.0" lang="en">
<h2 class="title editable block">
<span class="title-prefix">2.8</span> Review Exercises and Sample Exam</h2>
<div class="qandaset block" id="fwk-redden-ch02_s08_qs01" defaultlabel="number">
<h3 class="title">Review Exercises</h3>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd01">
<h3 class="title">Relations, Graphs, and Functions</h3>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd01_qd01">
<p class="para" id="fwk-redden-ch02_s08_qs01_p01"><strong class="emphasis bold">Determine the domain and range and state whether the function is a relation or not.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa01">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p02">{(−4, −1), (−5, 3), (10, 3), (11, 2), (15, 1)}</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa02">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p04">{(−3, 0), (−2, 1), (1, 3), (2, 7), (2, 5)}</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa03">
<div class="question">
<div class="informalfigure large">
<img src="section_05/a61f2c5f837df9a2a116562e3991567f.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa04">
<div class="question">
<div class="informalfigure large">
<img src="section_05/1ed756585e2258ea7d1e1d216300ce03.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa05">
<div class="question">
<div class="informalfigure large">
<img src="section_05/6bca3209efde75958e81d7a944b01c0f.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa06">
<div class="question">
<div class="informalfigure large">
<img src="section_05/c13508b8b1e2731cd179beeef1010d48.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa07">
<div class="question">
<div class="informalfigure large">
<img src="section_05/09e0fe607265a54a821df68b5a8da600.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa08">
<div class="question">
<div class="informalfigure large">
<img src="section_05/97028b434ef145d542b952ac78932c4d.png">
</div>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd01_qd02" start="9">
<p class="para" id="fwk-redden-ch02_s08_qs01_p18"><strong class="emphasis bold">Evaluate.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa09">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p19"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2020" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>x</mi><mo>−</mo><mn>3</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2021" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2022" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2023" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mrow><mn>4</mn><mi>a</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa10">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p21"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2027" display="inline"><mrow><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>4</mn><mo>−</mo><mi>x</mi></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2028" display="inline"><mrow><mi>p</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2029" display="inline"><mrow><mi>p</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2030" display="inline"><mrow><mi>p</mi><mrow><mo>(</mo><mrow><mn>5</mn><mi>a</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa11">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p23"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2034" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></math></span>; find <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2035" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2036" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2037" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mi>h</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa12">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p25"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2041" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>9</mn></mrow></math></span>; find <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2042" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2043" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2044" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mi>h</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa13">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p27"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2048" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msqrt><mrow><mn>2</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow></msqrt></mrow></math></span>; find <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2049" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2050" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2051" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mrow><mn>13</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa14">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p29"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2055" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mroot><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span>; find <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2056" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2057" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2058" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mrow><mn>21</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa15">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p31"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2062" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>8</mn><mi>x</mi><mo>+</mo><mn>3</mn></mrow></math></span>; find <em class="emphasis">x</em> where <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2063" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>10</mn></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa16">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p33"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2065" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>5</mn><mo>−</mo><mn>3</mn><mi>x</mi></mrow></math></span>; find <em class="emphasis">x</em> where <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2066" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>4</mn></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa17">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p35">Given the graph of <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2068" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> below, find <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2069" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>60</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2070" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2071" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mn>20</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
<div class="informalfigure large">
<img src="section_05/751d4e2986f76245f47b1ad041c342a4.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa18">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p38">Given the graph of <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2075" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> below, find <em class="emphasis">x</em> where <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2076" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>4</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2077" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>12</mn></mrow><mo>.</mo></math></span></p>
<div class="informalfigure large">
<img src="section_05/e9c737b5992119bbca37f6af559e0463.png">
</div>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd02">
<h3 class="title">Linear Functions and Their Graphs</h3>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd02_qd01" start="19">
<p class="para" id="fwk-redden-ch02_s08_qs01_p41"><strong class="emphasis bold">Graph and label the intercepts.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa19">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p42"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2081" display="inline"><mrow><mn>4</mn><mi>x</mi><mo>−</mo><mn>8</mn><mi>y</mi><mo>=</mo><mn>12</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa20">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p44"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2082" display="inline"><mrow><mn>9</mn><mi>x</mi><mo>+</mo><mn>4</mn><mi>y</mi><mo>=</mo><mn>6</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa21">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p46"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2083" display="inline"><mrow><mfrac><mn>3</mn><mn>8</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>y</mi><mo>=</mo><mfrac><mn>5</mn><mn>4</mn></mfrac></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa22">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p48"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2084" display="inline"><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>x</mi><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>y</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd02_qd02" start="23">
<p class="para" id="fwk-redden-ch02_s08_qs01_p50"><strong class="emphasis bold">Graph the linear function and label the <em class="emphasis">x</em>-intercept.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa23">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p51"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2085" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>5</mn><mn>8</mn></mfrac><mi>x</mi><mo>+</mo><mn>10</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa24">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p53"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2086" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mi>x</mi><mo>−</mo><mn>3</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa25">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p55"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2087" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa26">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p57"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2088" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>5</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa27">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p59"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2089" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa28">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p61"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2090" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>6</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd02_qd03" start="29">
<p class="para" id="fwk-redden-ch02_s08_qs01_p63"><strong class="emphasis bold">Find the slope of the line passing through the given points.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa29">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p64"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2091" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>5</mn><mo>,</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2092" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn><mo>,</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa30">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p66"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2094" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>7</mn><mo>,</mo><mo>−</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2095" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>9</mn><mo>,</mo><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa31">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p68"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2097" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2098" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>1</mn><mrow><mn>10</mn></mrow></mfrac><mo>,</mo><mo>−</mo><mfrac><mn>3</mn><mn>5</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa32">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p70"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2100" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>3</mn><mn>8</mn></mfrac><mo>,</mo><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2101" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>,</mo><mo>−</mo><mfrac><mn>1</mn><mrow><mn>16</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa33">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p72"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2103" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>14</mn><mo>,</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2104" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>10</mn><mo>,</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa34">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p74"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2106" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>6</mn><mo>,</mo><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2107" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>6</mn><mo>,</mo><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd02_qd04" start="35">
<p class="para" id="fwk-redden-ch02_s08_qs01_p76"><strong class="emphasis bold">Graph</strong> <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2108" display="inline"><mi>f</mi></math></span> <strong class="emphasis bold">and</strong> <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2109" display="inline"><mi>g</mi></math></span> <strong class="emphasis bold">on the same rectangular coordinate plane. Use the graph to find all values of <em class="emphasis">x</em> for which the given relation is true. Verify your answer algebraically.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa35">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p77"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2110" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>x</mi><mo>−</mo><mn>2</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2111" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mi>x</mi><mo>+</mo><mn>4</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2112" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa36">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p79"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2114" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>5</mn><mi>x</mi><mo>−</mo><mn>2</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2115" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>3</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2116" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≥</mo><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa37">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p81"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2118" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>3</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2119" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2120" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo><</mo><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa38">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p83"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2122" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mi>x</mi><mo>−</mo><mn>1</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2123" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mi>x</mi><mo>+</mo><mn>5</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2124" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≤</mo><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd03">
<h3 class="title">Modeling Linear Functions</h3>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd03_qd01" start="39">
<p class="para" id="fwk-redden-ch02_s08_qs01_p85"><strong class="emphasis bold">Find the linear function passing through the given points.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa39">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p86"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2126" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2127" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>−</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa40">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p88"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2129" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>,</mo><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2130" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn><mo>,</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa41">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p90"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2132" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>7</mn><mo>,</mo><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2133" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>5</mn><mo>,</mo><mo>−</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa42">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p92"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2135" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>5</mn><mo>,</mo><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2136" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn><mo>,</mo><mo>−</mo><mn>9</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa43">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p94">Find the equation of the given linear function:</p>
<div class="informalfigure large">
<img src="section_05/b507718cfbf1987b682736ad5f44f88f.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa44">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p97">Find the equation of the given linear function:</p>
<div class="informalfigure large">
<img src="section_05/18bee4c6b0c8396e1c9554830d34bf2e.png">
</div>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd03_qd02" start="45">
<p class="para" id="fwk-redden-ch02_s08_qs01_p100"><strong class="emphasis bold">Find the equation of the line:</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa45">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p101">Parallel to <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2140" display="inline"><mrow><mn>8</mn><mi>x</mi><mo>−</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>24</mn></mrow></math></span> and passing through <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2141" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>9</mn><mo>,</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa46">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p103">Parallel to <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2143" display="inline"><mrow><mn>6</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>24</mn></mrow></math></span> and passing through <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2144" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa47">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p105">Parallel to <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2146" display="inline"><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac><mi>x</mi><mo>−</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>y</mi><mo>=</mo><mn>1</mn></mrow></math></span> and passing through <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2147" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn><mo>,</mo><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa48">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p107">Perpendicular to <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2149" display="inline"><mrow><mn>14</mn><mi>x</mi><mo>+</mo><mn>7</mn><mi>y</mi><mo>=</mo><mn>10</mn></mrow></math></span> and passing through <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2150" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>8</mn><mo>,</mo><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa49">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p109">Perpendicular to <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2152" display="inline"><mrow><mn>15</mn><mi>x</mi><mo>−</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>6</mn></mrow></math></span> and passing through <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2153" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn><mo>,</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa50">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p111">Perpendicular to <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2155" display="inline"><mrow><mfrac><mn>2</mn><mn>9</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span> and passing through <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2156" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mo>,</mo><mo>−</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd03_qd03" start="51">
<p class="para" id="fwk-redden-ch02_s08_qs01_p113"><strong class="emphasis bold">Use algebra to solve the following.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa51">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p114">A taxi fare in a certain city includes an initial charge of $2.50 plus $2.00 per mile driven. Write a function that gives the cost of a taxi ride in terms of the number of miles driven. Use the function to determine the number of miles driven if the total fare is $9.70.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa52">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p116">A salesperson earns a base salary of $1,800 per month and 4.2% commission on her total sales for that month. Write a function that gives her monthly salary based on her total sales. Use the function to determine the amount of sales for a month in which her salary was $4,824.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa53">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p118">A certain automobile sold for $1,200 in 1980, after which it began to be considered a collector’s item. In 1994, the same automobile sold at auction for $5,750. Write a linear function that models the value of the automobile in terms of the number of years since 1980. Use it to estimate the value of the automobile in the year 2000.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa54">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p120">A specialized industrial robot was purchased new for $62,400. It has a lifespan of 12 years, after which it will be considered worthless. Write a linear function that models the value of the robot. Use the function to determine its value after 8 years of operation.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa55">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p122">In 1950, the U.S. Census Bureau estimated the population of Detroit, MI to be 1.8 million people. In 1990, the population was estimated to have decreased to 1 million. Write a linear function that gives the population of Detroit in millions of people, in terms of years since 1950. Use the function to estimate the year in which the population decreased to 700,000 people.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa56">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p124">Online sales of a particular product are related to the number of clicks on its advertisement. It was found that 100 clicks in a week result in $112 of online sales, and that 500 clicks result in $160 of online sales. Write a linear function that models the online sales of the product based on the number of clicks on its advertisement. How many clicks are needed to result in $250 of weekly online sales from this product?</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa57">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p126">The cost in dollars of producing <em class="emphasis">n</em> bicycles is given by the formula <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2164" display="inline"><mrow><mi>C</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>=</mo><mn>80</mn><mi>n</mi><mo>+</mo><mn>3,380</mn></mrow><mo>.</mo></math></span> If each bicycle can be sold for $132, write a function that gives the profit generated by producing and selling <em class="emphasis">n</em> bicycles. Use the formula to determine the number of bicycles that must be produced and sold to profit at least $10,000.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa58">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p128">Determine the breakeven point from the previous exercise.</p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd04">
<h3 class="title">Basic Functions</h3>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd04_qd01" start="59">
<p class="para" id="fwk-redden-ch02_s08_qs01_p130"><strong class="emphasis bold">Find the ordered pair that specifies the point <em class="emphasis">P</em>.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa59">
<div class="question">
<div class="informalfigure large">
<img src="section_05/cfe6c533a0e17b12184807ec35db49d7.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa60">
<div class="question">
<div class="informalfigure large">
<img src="section_05/2c800f862e8f0905d0c50866733110f9.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa61">
<div class="question">
<div class="informalfigure large">
<img src="section_05/5b9ccb492de957897ff12ddc30187931.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa62">
<div class="question">
<div class="informalfigure large">
<img src="section_05/0296c2f1606ec138e3240fca3f36f473.png">
</div>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd04_qd02" start="63">
<p class="para" id="fwk-redden-ch02_s08_qs01_p139"><strong class="emphasis bold">Graph the piecewise defined functions.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa63">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2170" display="block"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mtext> </mtext><msup><mi>x</mi><mn>2</mn></msup><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo><</mo><mn>5</mn></mtd></mtr><mtr><mtd><mn>10</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≥</mo><mn>5</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa64">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2171" display="block"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mo>−</mo><mn>5</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo><</mo><mo>−</mo><mn>5</mn></mtd></mtr><mtr><mtd><mtext> </mtext><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≥</mo><mo>−</mo><mn>5</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa65">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2172" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mtext> </mtext><mi>x</mi><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≤</mo><mo>−</mo><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>x</mi><mn>3</mn></msup><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>></mo><mo>−</mo><mn>1</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa66">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2173" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≤</mo><mn>4</mn></mtd></mtr><mtr><mtd><msqrt><mi>x</mi></msqrt><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>></mo><mn>4</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa67">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2174" display="block"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mtext> </mtext><mtext> </mtext><mi>x</mi><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo><</mo><mo>−</mo><mn>3</mn></mtd></mtr><mtr><mtd><mtext> </mtext><msup><mi>x</mi><mn>2</mn></msup><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mo>−</mo><mn>3</mn><mo>≤</mo><mi>x</mi><mo><</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>−</mo><mn>6</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≥</mo><mn>3</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa68">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2175" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mtext> </mtext><mn>1</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo><</mo><mo>−</mo><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mo>−</mo><mn>1</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>0</mn></mtd></mtr><mtr><mtd><mfrac><mn>1</mn><mi>x</mi></mfrac><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>></mo><mn>0</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa69">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2176" display="block"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mtext> </mtext><mtext> </mtext><mn>1</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≤</mo><mo>−</mo><mn>1</mn></mtd></mtr><mtr><mtd><mtext> </mtext><mtext> </mtext><mn>0</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mo>−</mo><mn>1</mn><mo><</mo><mi>x</mi><mo>≤</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>−</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>></mo><mn>1</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa70">
<div class="question">
<p class="para"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2177" display="inline"><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mpadded width="-0.2em"><mo stretchy="false">[</mo></mpadded><mo stretchy="false">[</mo><mi>x</mi><mpadded width="-0.2em"><mo stretchy="false">]</mo></mpadded><mo stretchy="false">]</mo><mo>+</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd04_qd03" start="71">
<p class="para" id="fwk-redden-ch02_s08_qs01_p156"><strong class="emphasis bold">Evaluate.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa71">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2178" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mn>5</mn><mi>x</mi><mo>−</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo><</mo><mo>−</mo><mn>6</mn></mtd></mtr><mtr><mtd><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><msup><mi>x</mi><mn>2</mn></msup><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≥</mo><mo>−</mo><mn>6</mn></mtd></mtr></mtable></mrow></mrow></math></span>
<p class="para">Find <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2179" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2180" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2181" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa72">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2185" display="block"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mn>2</mn><mo>−</mo><mn>5</mn><mi>x</mi><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≤</mo><mn>0</mn></mtd></mtr><mtr><mtd><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><msup><mi>x</mi><mn>3</mn></msup><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>></mo><mn>0</mn></mtd></mtr></mtable></mrow></mrow></math></span>
<p class="para">Find <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2186" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2187" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2188" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa73">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2192" display="block"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mtext> </mtext><mtext> </mtext><mo>−</mo><mn>5</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo><</mo><mo>−</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>−</mo><mn>9</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mo>−</mo><mn>4</mn><mo>≤</mo><mi>x</mi><mo><</mo><mn>0</mn></mtd></mtr><mtr><mtd><mtext> </mtext><mtext> </mtext><msqrt><mi>x</mi></msqrt><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≥</mo><mn>0</mn></mtd></mtr></mtable></mrow></mrow></math></span>
<p class="para">Find <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2193" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2194" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2195" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa74">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2199" display="block"><mrow><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mtext> </mtext><mtext> </mtext><mfrac><mn>1</mn><mi>x</mi></mfrac><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo><</mo><mo>−</mo><mn>1</mn></mtd></mtr><mtr><mtd><mtext> </mtext><mtext> </mtext><mn>0</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mo>−</mo><mn>1</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>1</mn></mtd></mtr><mtr><mtd><mtext> </mtext><mtext> </mtext><mi>x</mi><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>></mo><mn>1</mn></mtd></mtr></mtable></mrow></mrow></math></span>
<p class="para">Find <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2200" display="inline"><mrow><mi>q</mi><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>5</mn><mn>3</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2201" display="inline"><mrow><mi>q</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2202" display="inline"><mrow><mi>q</mi><mrow><mo>(</mo><mrow><mn>16</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd05">
<h3 class="title">Transformations</h3>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd05_qd01" start="75">
<p class="para" id="fwk-redden-ch02_s08_qs01_p165"><strong class="emphasis bold">Sketch the graph of the given function.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa75">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p166"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2206" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><mn>10</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa76">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p168"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2207" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msqrt><mrow><mi>x</mi><mo>−</mo><mn>6</mn></mrow></msqrt><mo>+</mo><mn>9</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa77">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p170"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2208" display="inline"><mrow><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>x</mi><mo>−</mo><mn>9</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa78">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p172"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2209" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa79">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p174"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2210" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>|</mo><mrow><mi>x</mi><mo>−</mo><mn>20</mn></mrow><mo>|</mo></mrow><mo>−</mo><mn>40</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa80">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p176"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2211" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow></mfrac></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa81">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p178"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2212" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>−</mo><mn>6</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa82">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p180"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2213" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mroot><mrow><mi>x</mi><mo>−</mo><mn>4</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>+</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa83">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2214" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><msup><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mo>)</mo></mrow><mn>2</mn></msup><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo><</mo><mo>−</mo><mn>2</mn></mtd></mtr><mtr><mtd><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>+</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≥</mo><mo>−</mo><mn>2</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa84">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2215" display="block"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mo>−</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo><</mo><mn>6</mn></mtd></mtr><mtr><mtd><mrow><mo>|</mo><mrow><mi>x</mi><mo>−</mo><mn>8</mn></mrow><mo>|</mo></mrow><mo>−</mo><mn>4</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>if</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>x</mi><mo>≥</mo><mn>6</mn></mtd></mtr></mtable></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa85">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p186"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2216" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mrow><mo>|</mo><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mo>|</mo></mrow><mo>−</mo><mn>8</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa86">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p188"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2217" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa87">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p190"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2218" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msqrt><mrow><mo>−</mo><mi>x</mi></mrow></msqrt><mo>−</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa88">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p192"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2219" display="inline"><mrow><mi>r</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>+</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa89">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p194"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2220" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>2</mn><mrow><mo>|</mo><mrow><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mo>|</mo></mrow><mo>+</mo><mn>8</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa90">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p196"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2221" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>5</mn><msqrt><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa91">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p198"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2222" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa92">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p200"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2223" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>3</mn></msup><mo>+</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd05_qd02" start="93">
<p class="para" id="fwk-redden-ch02_s08_qs01_p202"><strong class="emphasis bold">Write an equation that represents the function whose graph is given.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa93">
<div class="question">
<div class="informalfigure large">
<img src="section_05/66ce7db45a05d568a1bb90fd8cf7256b.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa94">
<div class="question">
<div class="informalfigure large">
<img src="section_05/c36e5b06b4611de9c2ca9f6296706d2d.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa95">
<div class="question">
<div class="informalfigure large">
<img src="section_05/bcc2ebd201dda91ed0936fd68c501d5e.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa96">
<div class="question">
<div class="informalfigure large">
<img src="section_05/dc3b6c5f2375ec353819b67f12bf3e49.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa97">
<div class="question">
<div class="informalfigure large">
<img src="section_05/e75628f49c69238d59de71f6afb9e124.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa98">
<div class="question">
<div class="informalfigure large">
<img src="section_05/a05ada75ba35cfe8d18cc9a72a58e1b2.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa99">
<div class="question">
<div class="informalfigure large">
<img src="section_05/1327ea37dbf140f3feeb1b3f6a6ac27d.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa100">
<div class="question">
<div class="informalfigure large">
<img src="section_05/bfe51dc10f3de0513b28f3872f048983.png">
</div>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd06">
<h3 class="title">Solving Absolute Value Equations and Inequalities</h3>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd06_qd01" start="101">
<p class="para" id="fwk-redden-ch02_s08_qs01_p219"><strong class="emphasis bold">Solve.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa101">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p220"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2232" display="inline"><mrow><mrow><mo>|</mo><mrow><mn>5</mn><mi>x</mi><mo>−</mo><mn>4</mn></mrow><mo>|</mo></mrow><mo>=</mo><mn>14</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa102">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p222"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2234" display="inline"><mrow><mrow><mo>|</mo><mrow><mn>4</mn><mo>−</mo><mn>3</mn><mi>x</mi></mrow><mo>|</mo></mrow><mo>=</mo><mn>4</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa103">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p224"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2236" display="inline"><mrow><mn>9</mn><mo>−</mo><mn>5</mn><mrow><mo>|</mo><mrow><mi>x</mi><mo>−</mo><mn>4</mn></mrow><mo>|</mo></mrow><mo>=</mo><mn>4</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa104">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p226"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2237" display="inline"><mrow><mn>6</mn><mo>+</mo><mn>2</mn><mrow><mo>|</mo><mrow><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mo>|</mo></mrow><mo>=</mo><mn>12</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa105">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p228"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2238" display="inline"><mrow><mrow><mo>|</mo><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mn>6</mn></mrow><mo>|</mo></mrow><mo>+</mo><mn>5</mn><mo>=</mo><mn>5</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa106">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p230"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2239" display="inline"><mrow><mn>0.2</mn><mrow><mo>|</mo><mrow><mi>x</mi><mo>−</mo><mn>1.8</mn></mrow><mo>|</mo></mrow><mo>=</mo><mn>4.6</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa107">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p232"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2240" display="inline"><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mrow><mo>|</mo><mrow><mn>2</mn><mi>x</mi><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>|</mo></mrow><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>=</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa108">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p234"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2242" display="inline"><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac><mrow><mo>|</mo><mrow><mi>x</mi><mo>+</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow><mo>|</mo></mrow><mo>−</mo><mn>2</mn><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa109">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p236"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2243" display="inline"><mrow><mrow><mo>|</mo><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mn>9</mn></mrow><mo>|</mo></mrow><mo>=</mo><mrow><mo>|</mo><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mo>|</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa110">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p238"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2245" display="inline"><mrow><mrow><mo>|</mo><mrow><mn>9</mn><mi>x</mi><mo>−</mo><mn>7</mn></mrow><mo>|</mo></mrow><mo>=</mo><mrow><mo>|</mo><mrow><mn>3</mn><mo>+</mo><mn>8</mn><mi>x</mi></mrow><mo>|</mo></mrow></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd06_qd02" start="111">
<p class="para" id="fwk-redden-ch02_s08_qs01_p240"><strong class="emphasis bold">Solve. Graph the solutions on a number line and give the corresponding interval notation.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa111">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p241"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2247" display="inline"><mrow><mrow><mo>|</mo><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mo>|</mo></mrow><mo><</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa112">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p243"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2249" display="inline"><mrow><mrow><mo>|</mo><mrow><mn>10</mn><mi>x</mi><mo>−</mo><mn>15</mn></mrow><mo>|</mo></mrow><mo>≤</mo><mn>25</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa113">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p245"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2251" display="inline"><mrow><mrow><mo>|</mo><mrow><mn>6</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>|</mo></mrow><mo>≤</mo><mn>11</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa114">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p247"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2253" display="inline"><mrow><mrow><mo>|</mo><mrow><mi>x</mi><mo>−</mo><mn>12</mn></mrow><mo>|</mo></mrow><mo>></mo><mn>7</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa115">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p249"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2255" display="inline"><mrow><mn>6</mn><mo>−</mo><mn>4</mn><mrow><mo>|</mo><mrow><mi>x</mi><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>|</mo></mrow><mo>≤</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa116">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p251"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2257" display="inline"><mrow><mn>5</mn><mo>−</mo><mrow><mo>|</mo><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mo>|</mo></mrow><mo>≥</mo><mn>4</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa117">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p253"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2259" display="inline"><mrow><mrow><mo>|</mo><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mo>|</mo></mrow><mo>+</mo><mn>7</mn><mo>≤</mo><mn>4</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa118">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p255"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2260" display="inline"><mrow><mn>2</mn><mrow><mo>|</mo><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow><mo>|</mo></mrow><mo>+</mo><mn>6</mn><mo>></mo><mn>4</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa119">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch02_m2262" display="block"><mrow><mn>5</mn><mrow><mo>|</mo><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>|</mo></mrow><mo>></mo><mfrac><mn>5</mn><mn>6</mn></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa120">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p259"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2264" display="inline"><mrow><mn>6.4</mn><mo>−</mo><mn>3.2</mn><mrow><mo>|</mo><mrow><mi>x</mi><mo>+</mo><mn>1.6</mn></mrow><mo>|</mo></mrow><mo>></mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd07">
<h3 class="title">Inequalities with Two Variables</h3>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd07_qd01" start="121">
<p class="para" id="fwk-redden-ch02_s08_qs01_p261"><strong class="emphasis bold">Is the ordered pair a solution to the given inequality?</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa121">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p262"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2266" display="inline"><mrow><mn>9</mn><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo><</mo><mo>−</mo><mn>1</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2267" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa122">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p264"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2268" display="inline"><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>y</mi><mo>></mo><mn>0</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2269" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mo>−</mo><mn>12</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa123">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p266"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2270" display="inline"><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>x</mi><mo>−</mo><mi>y</mi><mo>≥</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2271" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>−</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa124">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p268"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2272" display="inline"><mrow><mi>x</mi><mo>−</mo><mi>y</mi><mo>≤</mo><mo>−</mo><mn>6</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2273" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn><mo>,</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa125">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p270"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2274" display="inline"><mrow><mi>y</mi><mo>≤</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>3</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2275" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn><mo>,</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa126">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p272"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2276" display="inline"><mrow><mi>y</mi><mo>></mo><mrow><mo>|</mo><mrow><mi>x</mi><mo>−</mo><mn>6</mn></mrow><mo>|</mo></mrow><mo>+</mo><mn>10</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2277" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn><mo>,</mo><mn>12</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa127">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p274"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2278" display="inline"><mrow><mi>y</mi><mo><</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>3</mn></msup><mo>+</mo><mn>7</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2279" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa128">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p276"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2280" display="inline"><mrow><mi>y</mi><mo>≥</mo><msqrt><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></msqrt></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2281" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch02_s08_qs01_qd07_qd02" start="129">
<p class="para" id="fwk-redden-ch02_s08_qs01_p278"><strong class="emphasis bold">Graph the solution set.</strong></p>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa129">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p279"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2282" display="inline"><mrow><mi>x</mi><mo>+</mo><mi>y</mi><mo><</mo><mn>6</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa130">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p281"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2283" display="inline"><mrow><mn>2</mn><mi>x</mi><mo>−</mo><mn>3</mn><mi>y</mi><mo>≥</mo><mn>9</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa131">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p283"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2284" display="inline"><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mi>y</mi><mo>≤</mo><mn>6</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa132">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p285"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2285" display="inline"><mrow><mi>y</mi><mo>+</mo><mn>4</mn><mo>></mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa133">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p287"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2286" display="inline"><mrow><mi>x</mi><mo>−</mo><mn>6</mn><mo>≥</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa134">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p289"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2287" display="inline"><mrow><mo>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mi>y</mi><mo>></mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa135">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p291"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2288" display="inline"><mrow><mi>y</mi><mo>></mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><mn>3</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa136">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p293"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2289" display="inline"><mrow><mi>y</mi><mo>≤</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><mn>3</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa137">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p295"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2290" display="inline"><mrow><mi>y</mi><mo><</mo><mo>−</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>+</mo><mn>9</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa138">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p297"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2291" display="inline"><mrow><mi>y</mi><mo>></mo><mrow><mo>|</mo><mrow><mi>x</mi><mo>−</mo><mn>12</mn></mrow><mo>|</mo></mrow><mo>+</mo><mn>3</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa139">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p299"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2292" display="inline"><mrow><mi>y</mi><mo>≥</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa140">
<div class="question">
<p class="para" id="fwk-redden-ch02_s08_qs01_p301"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2293" display="inline"><mrow><mi>y</mi><mo>></mo><mo>−</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>3</mn></msup></mrow></math></span></p>
</div>
</li>
</ol>
</ol>
</div>
<div class="qandaset block" id="fwk-redden-ch02_s08_qs01_ans" defaultlabel="number">
<h3 class="title">Answers</h3>
<ol class="qandadiv">
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa01_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch02_s08_qs01_p03_ans">Domain: {−5, −4, 10, 11, 15}; range:{−1, 1, 2, 3}; function: yes</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa02_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa03_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch02_s08_qs01_p07_ans">Domain: {−5, 5, 15, 30}; range: {−5, 0, 5, 10, 15}; function: no</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa04_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa05_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch02_s08_qs01_p11_ans">Domain: <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2012" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mi>∞</mi><mo>,</mo><mi>∞</mi></mrow><mo>)</mo></mrow></mrow></math></span>; range: <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2013" display="inline"><mrow><mrow><mo>[</mo><mrow><mo>−</mo><mn>6</mn><mo>,</mo><mi>∞</mi></mrow><mo>)</mo></mrow></mrow></math></span>; function: yes</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa06_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa07_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch02_s08_qs01_p15_ans">Domain: <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2016" display="inline"><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mi>∞</mi><mo>,</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><mo>]</mo></mrow></mrow></math></span>; range: <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2017" display="inline"><mrow><mrow><mo>[</mo><mrow><mn>1</mn><mo>,</mo><mi>∞</mi></mrow><mo>)</mo></mrow></mrow></math></span>; function: yes</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa08_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa09_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch02_s08_qs01_p20_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2024" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>8</mn></mrow><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>7</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2025" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2026" display="inline"><mrow><mi>h</mi><mrow><mo>(</mo><mrow><mn>4</mn><mi>a</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>2</mn><mi>a</mi><mo>−</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa10_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa11_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch02_s08_qs01_p24_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2038" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>58</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2039" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mn>3</mn></mrow></math></span>, and <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2040" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mi>h</mi></mrow><mo>)</mo></mrow><mo>=</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mi>h</mi><mo>+</mo><mn>2</mn><msup><mi>h</mi><mn>2</mn></msup><mo>−</mo><mi>x</mi><mo>−</mo><mi>h</mi><mo>+</mo><mn>3</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa12_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa13_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch02_s08_qs01_p28_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2052" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow><mo>=</mo><mn>3</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2053" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2054" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mrow><mn>13</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>5</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa14_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa15_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch02_s08_qs01_p32_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2064" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mfrac><mn>7</mn><mn>8</mn></mfrac></mrow><mo>)</mo></mrow><mo>=</mo><mn>10</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa16_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa17_ans">
<div class="answer">
<p class="para" id="fwk-redden-ch02_s08_qs01_p37_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch02_m2072" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>60</mn></mrow><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>20</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2073" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mn>20</mn></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch02_m2074" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mn>20</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa18_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
</ol>
<ol class="qandadiv" start="19">
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa19_ans">
<div class="answer">
<div class="informalfigure large">
<img src="section_05/d51568b8aacba97ad21f9b0d9f14f954.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa20_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa21_ans">
<div class="answer">
<div class="informalfigure large">
<img src="section_05/a3cdd7fc127769413cc058e7351788d2.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa22_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa23_ans">
<div class="answer">
<div class="informalfigure large">
<img src="section_05/931e3f021377c605cb3046e51e289f7a.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa24_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa25_ans">
<div class="answer">
<div class="informalfigure large">
<img src="section_05/24a0d3fe843539e8a8a63fd2d44162db.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa26_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa27_ans">
<div class="answer">
<div class="informalfigure large">
<img src="section_05/ac99829520bad1115ac0508fa83efc90.png">
</div>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch02_s08_qs01_qa28_ans" audience="instructoronly">
<div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
</div>