chap2-rev-problems.xml

<?xml version="1.0"?>


<!-- This file was originally part of the book     -->
<!--   Modeling, Functions, and Graphs   -->
<!--           4th                                     -->
<!-- Copyright (C) Katherine Yoshiwara      -->

<exercises xml:id="chap2-rev-problems"  xmlns:xi="http://www.w3.org/2001/XInclude">
    <title>Review Problems</title>

<exercisegroup cols="2">
        <introduction><p>Solve by extraction of roots.</p></introduction>

    <exercise number="1">
        <statement><p><m>(2x - 5)^2 = 9</m></p></statement>
        <answer><p><m>x = 1</m> or <m>x = 4</m></p></answer>
    </exercise>

    <exercise number="2">
        <statement><p><m>(7x - 1)^2 = 15</m></p></statement>
    </exercise>

    <exercise number="3">
        <statement><p><m>6\left(\dfrac{w-1}{3} \right)^2- 4 = 2</m></p></statement>
    <answer><p><m>w = -2</m> or <m>w = 4</m> </p></answer>
    </exercise>

    <exercise number="4">
        <statement><p><m>\left(\dfrac{2p}{5} \right)^2=-3 </m></p></statement>
    </exercise>
</exercisegroup>

<exercisegroup cols="2"><introduction><p>Solve the formulas for the specified variable.</p></introduction>

    <exercise number="5">
        <statement><p><m>A = P(1 + r )^2</m> , for <m>r</m></p></statement>
        <answer><p><m>r = -1 \pm \sqrt{\dfrac{A}{P}}</m></p></answer>
    </exercise>

    <exercise number="6">
        <statement><p><m>V = \dfrac{4}{3}\pi r^3</m>, for <m>r</m></p></statement>
    </exercise>

</exercisegroup>

<exercise number="7"><statement><p>Lewis invested <m>\$2000</m> in an account that compounds interest annually. He made no deposits or withdrawals after that. Two years later, he closed the account, withdrawing <m>\$2464.20</m>. What interest rate did Lewis earn?</p></statement>
<answer><p><m>11\%</m></p></answer>
</exercise>

<exercise number="8"><statement><p>Earl borrowed <m>\$5500</m> from his uncle for two years with interest compounded annually. At the end of two years, he owed his uncle <m>\$6474.74</m>. What was the interest rate
on the loan?</p></statement></exercise>

<exercisegroup cols="2"><introduction><p>Solve.</p></introduction>
    <exercise number="9"><statement><p><m>\sqrt[3]{P-1}=0.1 </m></p></statement>
    <answer><p><m>P = 1.001</m></p></answer>
    </exercise>

    <exercise number="10"><statement><p><m>\dfrac{1}{1 - t}= \dfrac{2}{3}</m></p></statement>
    </exercise>

    <exercise number="11"><statement><p><m>\dfrac{3}{\sqrt{m+7}}=\dfrac{1}{2} </m></p></statement>
    <answer><p><m>m = 29</m></p></answer>
    </exercise>

    <exercise number="12"><statement><p><m>15 = 3\sqrt{w + 1}</m></p></statement></exercise>

    <exercise number="13"><statement><p><m>4r^3 - 8 = 100</m></p></statement>
    <answer><p><m>r = 3</m></p></answer>
    </exercise>

    <exercise number="14"><statement><p><m>5s^2 + 6 = 3s^2 + 31</m></p></statement></exercise>

</exercisegroup>

<exercisegroup><introduction><p>Use the Pythagorean theorem to write and solve an equation.</p></introduction>
    <exercise number="15"><statement><p>A widescreen television measures <m>96</m> cm by <m>54</m> cm. How long is the diagonal?</p></statement>
    <answer><p><m>\sqrt{12132}\approx 110</m> cm</p></answer>
    </exercise>

    <exercise><statement><p>A <m>15</m>-foot ladder leans to the top of a <m>12</m>-foot fence. How far is the foot of the ladder from the base of the fence?</p></statement></exercise>
</exercisegroup>

<exercisegroup cols="2"><introduction><p>Simplify.</p></introduction>
    <exercise number="17"><statement><p><m>\abs{-18}-\abs{20} </m></p></statement>
    <answer><p><m>-2</m></p></answer>
    </exercise>

    <exercise number="18"><statement><p><m>\abs{-2\cdot(3-18)} </m></p></statement></exercise>

    <exercise number="19"><statement><p><m>\abs{-2\cdot 3 - 18} </m></p></statement>
    <answer><p><m>24</m></p></answer>
    </exercise>

    <exercise number="20"><statement><p><m>-2\cdot \abs{3-18} </m></p></statement></exercise>
</exercisegroup>

<exercisegroup><introduction><p>Use the graph to solve the equation or inequality</p></introduction>
    <exercise number="21"><statement><p>
        Refer to the graph of <m>y = \abs{\dfrac{x}{2}-1}</m>
        <image source="images/fig-chap2-rev-21"  width="35%">
          <description>
            abs(x/2-1)
          </description>
        </image>
        <ol>
            <li><p>Solve <m>\abs{\dfrac{x}{2}-1}=2</m></p></li>
            <li><p>Solve <m>\abs{\dfrac{x}{2}-1}\lt 2</m></p></li>
            <li><p>Solve <m>\abs{\dfrac{x}{2}-1}\ge 2</m></p></li>
        </ol>
    </p></statement>
    <answer><p>
        <ol label="a" cols="3">
            <li><p><m>x = -2</m> or <m>x = 6</m></p></li>
            <li><p><m>(-2, 6)</m></p></li>
            <li><p><m>(-\infty,-2] \cup [6,+\infty)</m></p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="22"><statement><p>
        Refer to the graph of <m>y = \dfrac{-x^2}{2}+x+1</m>
        <image source="images/fig-chap2-rev-22"  width="35%">
          <description>
            curve
          </description>
        </image>
        <ol>
            <li><p>Solve <m>\dfrac{-x^2}{2}+x+1=-3</m></p></li>
            <li><p>Solve <m>\dfrac{-x^2}{2}+x+1\ge -3</m></p></li>
            <li><p>Solve <m>\dfrac{-x^2}{2}+x+1\le -3</m></p></li>
        </ol>
    </p></statement>
    </exercise>

    <exercise number="23"><statement><p>
        Refer to the graph of <m>y = \dfrac{6}{x^2-3x+3}</m>
        <image source="images/fig-chap2-rev-23"  width="30%">
          <description>
            abs(x/2-1)
          </description>
        </image>
        <ol>
            <li><p>Solve <m>2=\dfrac{6}{x^2-3x+3}</m></p></li>
            <li><p>Solve <m>2\gt\dfrac{6}{x^2-3x+3}</m></p></li>
            <li><p>Solve <m>2\lt\dfrac{6}{x^2-3x+3}</m></p></li>
        </ol>
    </p></statement>
    <answer><p>
        <ol label="a" cols="3">
            <li><p><m>x = 0</m> or <m>x = 3</m></p></li>
            <li><p><m>(0, 3)</m></p></li>
            <li><p><m>(-\infty,0) \cup (3,\infty)</m></p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="24"><statement><p>
        Refer to the graph of <m>y = \abs{x^3 + 3x^2 + 3x +1}</m>
        <image source="images/fig-chap2-rev-24"  width="35%">
          <description>
            curve
          </description>
        </image>
        <ol>
            <li><p>Solve <m>8=\abs{x^3 + 3x^2 + 3x +1}</m></p></li>
            <li><p>Solve <m>8\gt\abs{x^3 + 3x^2 + 3x +1}</m></p></li>
            <li><p>Solve <m>8\lt\abs{x^3 + 3x^2 + 3x +1}</m></p></li>
        </ol>
    </p></statement>
    </exercise>
</exercisegroup>


<exercisegroup cols="2"><introduction><p>Graph each piecewise defined function.</p></introduction>
    <exercise number="25"><statement><p><m>
        f(x) =
        \begin{cases}
        x+1 \amp \text{if } x\le 0\\
        x^2  \amp \text{if } x\gt 0
        \end{cases}
    </m></p></statement>
    <answer><p><image source="images/fig-ans-chap2-rev-25"  width="40%"><description>piecewise defined function</description></image> </p></answer>
    </exercise>

    <exercise number="26"><statement><p><m>
        g(x) =
        \begin{cases}
        x-1 \amp \text{if } x\le 1\\
        x^3  \amp \text{if } x\gt 1
        \end{cases}
    </m></p></statement>
    </exercise>

    <exercise number="27"><statement><p><m>
        H(x) =
        \begin{cases}
        x^2 \amp \text{if } x\le 0\\
        \sqrt{x}  \amp \text{if } x\gt 0
        \end{cases}
    </m></p></statement>
    <answer><p><image source="images/fig-ans-chap2-rev-27"  width="40%"><description>piecewise defined function</description></image> </p></answer>
    </exercise>

    <exercise number="28"><statement><p><m>
        F(x) =
        \begin{cases}
        \abs{x} \amp \text{if } x\le 0\\
        \dfrac{1}{x}  \amp \text{if } x\gt 0
        \end{cases}
    </m></p></statement>
    </exercise>

    <exercise number="29"><statement><p><m>
        S(x) =
        \begin{cases}
        x^3 \amp \text{if } x\le 1\\
        \abs{x}  \amp \text{if } x\gt 1
        \end{cases}
    </m></p></statement>
    <answer><p><image source="images/fig-ans-chap2-rev-29"  width="40%"><description>piecewise defined function</description></image> </p></answer>
    </exercise>

    <exercise number="30"><statement><p><m>
        T(x) =
        \begin{cases}
        \dfrac{1}{x^2} \amp \text{if } x\lt 0\\
        \sqrt{x}  \amp \text{if } x\ge 0
        \end{cases}
    </m></p></statement>
    </exercise>
</exercisegroup>


<exercisegroup cols="2"><introduction><p>For Problems 31–38,
    <ol label="a">
        <li><p>Describe each function as transformation of a basic function.</p></li>
        <li><p>Sketch a graph of the basic function and the given function on the same axes.</p></li>
    </ol>
</p></introduction>

    <exercise number="31"><statement><p><m>g(x) = \abs{x} + 2</m></p></statement>
    <answer><p>
        <ol label="a" cols="2">
            <li><p><m>y =\abs{x}</m> shifted up <m>2</m> units</p></li>
            <li><p><image source="images/fig-ans-chap2-rev-31"  width="80%"><description>shifted absolute value</description></image> </p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="32"><statement><p><m>F(t) = \dfrac{1}{t}- 2</m></p></statement>
    </exercise>

    <exercise number="33"><statement><p><m>f (s) =\sqrt{s} + 3</m></p></statement>
    <answer><p>
        <ol label="a" cols="2">
            <li><p><m>y =\sqrt{x}</m> shifted up <m>3</m> units</p></li>
            <li><p><image source="images/fig-ans-chap2-rev-33"  width="80%"><description>shifted square root</description></image> </p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="34"><statement><p><m>g(u) =\sqrt{u + 2} - 3</m></p></statement>
    </exercise>

    <exercise number="35"><statement><p><m>G(t) = \abs{t + 2} - 3</m></p></statement>
    <answer><p>
        <ol label="a" cols="2">
            <li><p><m>y =\abs{x}</m> shifted left <m>2</m> units and down <m>3</m> units</p></li>
            <li><p><image source="images/fig-ans-chap2-rev-35"  width="80%"><description>shifted absolute value</description></image> </p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="36"><statement><p><m>H(t) = \dfrac{1}{(t - 2)^2}+ 3</m></p></statement>
    </exercise>

    <exercise number="37"><statement><p><m>h(s) = -2\sqrt{s} </m></p></statement>
    <answer><p>
        <ol label="a" cols="2">
            <li><p><m>y =\sqrt{x}</m> reflected across the horizontal axis and stretched vertically by a factor of <m>2</m></p></li>
            <li><p><image source="images/fig-ans-chap2-rev-37"  width="80%"><description>reflected and stretched square root</description></image> </p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="38"><statement><p><m>H(t) = \dfrac{1}{ 2}\abs{s} </m></p></statement>
    </exercise>
</exercisegroup>


<exercisegroup><introduction><p>In Problems 39–42, write a formula for each transformation of the given function.</p></introduction>

    <exercise number="39"><statement><p>
        <image source="images/fig-chap2-rev-39"  width="80%">
          <description>
            curve and three transformations
          </description>
        </image>
    </p></statement>
    <answer><p>
        <ol label="a" cols="3">
            <li><p><m>y =\dfrac{-3}{2}f (t)</m></p></li>
            <li><p><m>y =\dfrac{-3}{2}f (t)+3</m></p></li>
            <li><p><m>y =\dfrac{-3}{2}f (t+2)+3</m></p></li>
        </ol>
    </p></answer>
    </exercise>


    <exercise number="40"><statement><p>
        <image source="images/fig-chap2-rev-40"  width="80%">
          <description>
            curve and three transformations
          </description>
        </image>
    </p></statement>
    </exercise>

    <exercise number="41"><statement><p>
        <tabular halign="center" top="major" right="minor" left="minor" bottom="minor">
            <row>
                <cell><m>t</m></cell>
                <cell><m>0</m></cell>
                <cell><m>1</m></cell>
                <cell><m>2</m></cell>
                <cell><m>3</m></cell>
                <cell><m>4</m></cell>
                <cell><m>5</m></cell>
            </row>
            <row>
                <cell><m>f(t)</m></cell>
                <cell><m>243</m></cell>
                <cell><m>81</m></cell>
                <cell><m>27</m></cell>
                <cell><m>9</m></cell>
                <cell><m>3</m></cell>
                <cell><m>1</m></cell>
            </row>
        </tabular>
        <ol label="a">
            <li><p>
                <tabular halign="center" top="major" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>t</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>4</m></cell>
                        <cell><m>5</m></cell>
                        <cell><m>6</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>243</m></cell>
                        <cell><m>81</m></cell>
                        <cell><m>27</m></cell>
                        <cell><m>9</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>1</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p>
                <tabular halign="center" top="major" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>t</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>4</m></cell>
                        <cell><m>5</m></cell>
                        <cell><m>6</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>-243</m></cell>
                        <cell><m>-81</m></cell>
                        <cell><m>-27</m></cell>
                        <cell><m>-9</m></cell>
                        <cell><m>-3</m></cell>
                        <cell><m>-1</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p>
                <tabular halign="center" top="major" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>t</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>4</m></cell>
                        <cell><m>5</m></cell>
                        <cell><m>6</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>57</m></cell>
                        <cell><m>219</m></cell>
                        <cell><m>273</m></cell>
                        <cell><m>291</m></cell>
                        <cell><m>297</m></cell>
                        <cell><m>299</m></cell>
                    </row>
                </tabular>
            </p></li>
        </ol>
    </p></statement>
    <answer><p>
        <ol label="a" cols="3">
            <li><p><m>y = f (t - 1)</m></p></li>
            <li><p><m>y = -f (t - 1)</m></p></li>
            <li><p><m>y = -f (t - 1)+300</m></p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="42"><statement><p>
        <tabular halign="center" top="major" right="minor" left="minor" bottom="minor">
            <row>
                <cell><m>x</m></cell>
                <cell><m>1</m></cell>
                <cell><m>2</m></cell>
                <cell><m>3</m></cell>
                <cell><m>4</m></cell>
                <cell><m>5</m></cell>
                <cell><m>6</m></cell>
            </row>
            <row>
                <cell><m>f(x)</m></cell>
                <cell><m>25</m></cell>
                <cell><m>24</m></cell>
                <cell><m>21</m></cell>
                <cell><m>16</m></cell>
                <cell><m>9</m></cell>
                <cell><m>0</m></cell>
            </row>
        </tabular>
        <ol label="a">
            <li><p>
                <tabular halign="center" top="major" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>-1</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>4</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>25</m></cell>
                        <cell><m>24</m></cell>
                        <cell><m>21</m></cell>
                        <cell><m>16</m></cell>
                        <cell><m>9</m></cell>
                        <cell><m>0</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p>
                <tabular halign="center" top="major" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>-1</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>4</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>50</m></cell>
                        <cell><m>48</m></cell>
                        <cell><m>42</m></cell>
                        <cell><m>32</m></cell>
                        <cell><m>18</m></cell>
                        <cell><m>0</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p>
                <tabular halign="center" top="major" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>-1</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>4</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>70</m></cell>
                        <cell><m>68</m></cell>
                        <cell><m>62</m></cell>
                        <cell><m>52</m></cell>
                        <cell><m>38</m></cell>
                        <cell><m>20</m></cell>
                    </row>
                </tabular>
            </p></li>
        </ol>
    </p></statement>
    </exercise>

</exercisegroup>


<exercisegroup cols="2"><introduction><p>Give an equation for the function graphed.</p></introduction>

    <exercise number="43"><statement><p><image source="images/fig-chap2-rev-43"  width="65%"><description>curve</description></image></p></statement>
    <answer><p><m>y = (x - 2)^2 - 4</m></p></answer> 
    </exercise>

    <exercise number="44"><statement><p><image source="images/fig-chap2-rev-44"  width="65%"><description>curve</description></image></p></statement>
    </exercise>
</exercisegroup>


<exercisegroup><introduction><p>Sketch graphs to illustrate the situations in Problems 45 and 46.</p></introduction>

    <exercise number="45"><statement><p>Inga runs hot water into the bathtub until it is about half full. Because the water is too hot, she lets it sit for a while before getting into the tub. After several minutes of bathing, she gets out and drains the tub. Graph the water level in the bathtub as a function of time, from the moment Inga starts filling the tub until it is drained.</p></statement>
    <answer><p><image source="images/fig-ans-chap2-rev-45"  width="50%"><description>curve</description></image> </p></answer>
    </exercise>

    <exercise number="46"><statement><p>David turns on the oven and it heats up steadily until the proper baking temperature is reached. The oven maintains that temperature during the time David bakes a pot roast. When he turns the oven off, David leaves the oven door open for a few minutes, and the temperature drops fairly rapidly during that time. After David closes the door, the temperature continues to drop, but at a much slower rate. Graph the temperature of the oven as a function of time, from the moment David first turns on the oven until shortly after David closes the door when the oven is cooling.</p></statement>
    </exercise>
</exercisegroup>


<exercisegroup><introduction><p>Match each table with its graph.</p></introduction>
    <exercise number="47"><statement><p>
        <ol label="*I*"  cols="2">
            <li><p>
                <tabular halign="center" left="minor" right="minor" bottom="minor" top="major">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>4</m></cell>
                        <cell><m>6</m></cell>
                        <cell><m>8</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>10</m></cell>
                        <cell><m>14</m></cell>
                        <cell><m>21</m></cell>
                        <cell><m>30</m></cell>
                        <cell><m>43</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p>
                <tabular halign="center" left="minor" right="minor" bottom="minor" top="major">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>10</m></cell>
                        <cell><m>20</m></cell>
                        <cell><m>30</m></cell>
                        <cell><m>40</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>20</m></cell>
                        <cell><m>52</m></cell>
                        <cell><m>65</m></cell>
                        <cell><m>75</m></cell>
                        <cell><m>83</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p>
                <tabular halign="center" left="minor" right="minor" bottom="minor" top="major">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>4</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>140</m></cell>
                        <cell><m>190</m></cell>
                        <cell><m>240</m></cell>
                        <cell><m>290</m></cell>
                        <cell><m>340</m></cell>
                    </row>
                </tabular>
            </p></li>
        </ol>
        <image source="images/fig-chap2-rev-47"  width="50%">
          <description>
            three increasing curves
          </description>
        </image>
    </p></statement>
    <answer><p>I (c), II (b), III (a)</p></answer>
    </exercise>

    <exercise number="48"><statement><p>
        <ol label="*I*" cols="2">
            <li><p>
                <tabular halign="center" left="minor" right="minor" bottom="minor" top="major">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>0.1</m></cell>
                        <cell><m>0.2</m></cell>
                        <cell><m>0.3</m></cell>
                        <cell><m>0.4</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>100</m></cell>
                        <cell><m>95</m></cell>
                        <cell><m>80</m></cell>
                        <cell><m>55</m></cell>
                        <cell><m>20</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p>
                <tabular halign="center" left="minor" right="minor" bottom="minor" top="major">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>4</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>8.5</m></cell>
                        <cell><m>7.1</m></cell>
                        <cell><m>5.7</m></cell>
                        <cell><m>4.3</m></cell>
                        <cell><m>2.9</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p>
                <tabular halign="center" left="minor" right="minor" bottom="minor" top="major">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>10</m></cell>
                        <cell><m>20</m></cell>
                        <cell><m>30</m></cell>
                        <cell><m>40</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>50</m></cell>
                        <cell><m>37</m></cell>
                        <cell><m>27</m></cell>
                        <cell><m>20</m></cell>
                        <cell><m>15</m></cell>
                    </row>
                </tabular>
            </p></li>
        </ol>
        <image source="images/fig-chap2-rev-48"  width="50%">
          <description>
            three decreasing curves
          </description>
        </image>
    </p></statement>
    </exercise>
</exercisegroup>


<exercisegroup><introduction><p>Write and graph a piecewise function for Problems 49 and 50.</p></introduction>
    <exercise number="49"><statement><p>The fluid level in a tank is a function of the number of days since the year began. The level was initially at <m>60</m> inches and rose an inch a day for <m>10</m> days, remained constant for the next <m>20</m> days, then dropped a half-inch each day for <m>30</m> days.</p></statement>
    <answer><p><m>
        g(t) =
        \begin{cases}
        60+t, \amp  0\le t \lt 10\\
        70, \amp 10\le t \lt 30\\
        70 - \frac{1}{2}(t - 30),  \amp 30\le t \le 60
        \end{cases}
    </m>
    <image source="images/fig-ans-chap2-rev-49"  width="45%">
      <description>
        piecewise
      </description>
    </image>
    </p></answer>
    </exercise>

    <exercise number="50"><statement><p>The temperature at different locations in a large room is a function of distance from the window. Within <m>2</m> feet of the window, the temperature is <m>66\degree</m> Fahrenheit, but the temperature rises by <m>0.5\degree</m> for each of the next <m>10</m> feet, then maintains the temperature at <m>12</m> feet for the rest of the room.</p></statement></exercise>
</exercisegroup>



<exercisegroup cols="2"><introduction><p>Use absolute value notation to write each expression as an equation or inequality.</p></introduction>
    <exercise number="51"><statement><p><m>x</m> is four units from the origin.</p></statement>
    <answer><p><m>\abs{x}=4 </m></p></answer>
    </exercise>

    <exercise number="52"><statement><p>The distance from <m>y</m> to <m>-5</m> is three units.</p></statement>
    </exercise>

    <exercise number="53"><statement><p><m>p</m> is within four units of <m>7</m>.</p></statement>
    <answer><p><m>\abs{p-7}\lt 4 </m></p></answer>
    </exercise>

    <exercise number="54"><statement><p><m>q</m> is at least <m>\dfrac{3}{10}</m> unit from <m>-4</m>.</p></statement>
    </exercise>
</exercisegroup>



<exercisegroup cols="2"><introduction><p>Solve.</p></introduction>
    <exercise number="55"><statement><p><m>\abs{9 - 5t} = 3</m></p></statement>
    <answer><p><m>t = \dfrac{6}{5}</m> or <m>t = \dfrac{12}{5}</m> </p></answer>
    </exercise>

    <exercise number="56"><statement><p><m>1=\abs{4q-7} </m></p></statement>
    </exercise>

    <exercise number="57"><statement><p><m>-29=\abs{2w + 3}</m></p></statement>
    <answer><p>No solutions </p></answer>
    </exercise>

    <exercise number="58"><statement><p><m>\abs{\dfrac{8n+3}{5}}=-11 </m></p></statement>
    </exercise>

    <exercise number="59"><statement><p><m>1=\abs{\dfrac{7-2p}{5}}</m></p></statement>
    <answer><p><m>p = 1</m> or <m>p = 6</m></p></answer>
    </exercise>

    <exercise number="60"><statement><p><m>\abs{6(r-10)}=30 </m></p></statement>
    </exercise>

    <exercise number="61"><statement><p><m>\abs{3x-2}\lt 4</m></p></statement>
    <answer><p><m>\left(\dfrac{-2}{3}, 2\right)</m></p></answer>
    </exercise>

    <exercise number="62"><statement><p><m>\abs{2x + 0.3}\le  0.5 </m></p></statement>
    </exercise>

    <exercise number="63"><statement><p><m>\abs{3y + 1.2}\ge 1.5</m></p></statement>
    <answer><p><m>(-\infty,-0.9] \cup [0.1,\infty)</m></p></answer>
    </exercise>

    <exercise number="64"><statement><p><m>\abs{3z+\dfrac{1}{2}}\gt  \dfrac{1}{3} </m></p></statement>
    </exercise>
</exercisegroup>



<exercisegroup cols="2"><introduction><p>Express the error tolerance using absolute value.</p></introduction>
    <exercise number="65"><statement><p>The height, <m>H</m>, of a female trainee must be between <m>56</m> inches and <m>75</m> inches.</p></statement>
    <answer><p><m>\abs{H - 65.5}\lt 9.5</m></p></answer>
    </exercise>

    <exercise number="66"><statement><p>The time, <m>t</m>, in freefall must be at least <m>3.5</m> seconds but no more than <m>8.1</m> seconds.</p></statement>
    </exercise>
</exercisegroup>



<exercisegroup cols="2"><introduction><p>Give an interval of possible values for the measurement.</p></introduction>
    <exercise number="67"><statement><p>The mass, <m>M</m>, of the sample must satisfy <m>\abs{M - 2.1}\le 0.05</m>.</p></statement>
    <answer><p><m>[2.05, 2.15]</m></p></answer>
    </exercise>

    <exercise number="68"><statement><p>The temperature, <m>T</m>, of the refrigerator is specified by <m>\abs{T - 4.0}\lt 0.5</m>.</p></statement>
    </exercise>
</exercisegroup>



<exercisegroup cols="2"><introduction><p>In Problems 69 and 70,
    <ol label="a">
        <li><p>Plot the points and sketch a smooth curve through them.</p></li>
        <li><p>Use your graph to help you discover the equation that describes the function.</p></li>
    </ol>
    </p></introduction>

    <exercise number="69"><statement><p>
        <tabular halign="center" left="minor" right="minor" bottom="minor" top="major">
            <row>
                <cell><m>x</m></cell>
                <cell><m>g(x)</m></cell>
            </row>
            <row>
                <cell><m>2</m></cell>
                <cell><m>12</m></cell>
            </row>
            <row>
                <cell><m>3</m></cell>
                <cell><m>8</m></cell>
            </row>
            <row>
                <cell><m>4</m></cell>
                <cell><m>6</m></cell>
            </row>
            <row>
                <cell><m>6</m></cell>
                <cell><m>4</m></cell>
            </row>
            <row>
                <cell><m>8</m></cell>
                <cell><m>3</m></cell>
            </row>
            <row>
                <cell><m>12</m></cell>
                <cell><m>2</m></cell>
            </row>
        </tabular>
    </p></statement>
    <answer><p>
        <ol label="a" cols="2">
            <li><p><image source="images/fig-ans-chap2-rev-69"  width="80%"><description>curve</description></image> </p></li>
            <li><p><m>g(x)=\dfrac{24}{x} </m></p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="70"><statement><p>
        <tabular halign="center" left="minor" right="minor" bottom="minor" top="major">
            <row>
                <cell><m>x</m></cell>
                <cell><m>F(x)</m></cell>
            </row>
            <row>
                <cell><m>-2</m></cell>
                <cell><m>8</m></cell>
            </row>
            <row>
                <cell><m>-1</m></cell>
                <cell><m>1</m></cell>
            </row>
            <row>
                <cell><m>0</m></cell>
                <cell><m>0</m></cell>
            </row>
            <row>
                <cell><m>1</m></cell>
                <cell><m>-1</m></cell>
            </row>
            <row>
                <cell><m>2</m></cell>
                <cell><m>-8</m></cell>
            </row>
            <row>
                <cell><m>3</m></cell>
                <cell><m>-27</m></cell>
            </row>
        </tabular>
    </p></statement>
    </exercise>
</exercisegroup>



<exercisegroup cols="2"><introduction><p>In Problems 71<ndash/>76,
    <ol label="a">
        <li><p>Use the graph to complete the table of values.</p></li>
        <li><p>By finding a pattern in the table of values, write an equation for the graph.</p></li>
    </ol>
    </p></introduction>

    <exercise number="71"><statement><p>
        <sidebyside width="70%"><image source="images/fig-chap2-rev-71"><description>line</description></image></sidebyside></p><p>
        <sidebyside><tabular halign="center" left="minor" right="minor" top="minor" bottom="minor">
            <row>
                <cell><m>x</m></cell>
                <cell><m>0</m></cell>
                <cell><m>4</m></cell>
                <cell><m>8</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>16</m></cell>
                <cell><m>\hphantom{000}</m></cell>
            </row>
            <row>
                <cell><m>y</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>10</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>2</m></cell>
            </row>
        </tabular></sidebyside>
    </p></statement>
    <answer><p>
        <ol label="a">
            <li><p>
                <tabular halign="center" left="minor" right="minor" top="minor" bottom="minor">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>4</m></cell>
                        <cell><m>8</m></cell>
                        <cell><m>\alert{14}</m></cell>
                        <cell><m>16</m></cell>
                        <cell><m>\alert{22}</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>\alert{24}</m></cell>
                        <cell><m>\alert{20}</m></cell>
                        <cell><m>\alert{16}</m></cell>
                        <cell><m>10</m></cell>
                        <cell><m>\alert{8}</m></cell>
                        <cell><m>2</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p><m>y = 24 - x</m></p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="72"><statement><p>
        <sidebyside width="70%"><image source="images/fig-chap2-rev-72"><description>line</description></image></sidebyside></p><p>
        <sidebyside><tabular halign="center" left="minor" right="minor" top="minor" bottom="minor">
            <row>
                <cell><m>x</m></cell>
                <cell><m>0</m></cell>
                <cell><m>4</m></cell>
                <cell><m>10</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>14</m></cell>
                <cell><m>\hphantom{000}</m></cell>
            </row>
            <row>
                <cell><m>y</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>18</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>24</m></cell>
            </row>
        </tabular></sidebyside>
    </p></statement>
    </exercise>

    <exercise number="73"><statement><p>
        <sidebyside width="70%"><image source="images/fig-chap2-rev-73"><description>curve</description></image></sidebyside></p><p>
        <sidebyside><tabular halign="center" left="minor" right="minor" top="minor" bottom="minor">
            <row>
                <cell><m>x</m></cell>
                <cell><m>0</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>4</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>16</m></cell>
                <cell><m>25</m></cell>
            </row>
            <row>
                <cell><m>y</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>1</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>3</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
            </row>
        </tabular></sidebyside>
    </p></statement>
    <answer><p>
        <ol label="a">
            <li><p>
                <tabular halign="center" left="minor" right="minor" top="minor" bottom="minor">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>\alert{1}</m></cell>
                        <cell><m>4</m></cell>
                        <cell><m>\alert{9}</m></cell>
                        <cell><m>16</m></cell>
                        <cell><m>25</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>\alert{0}</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>\alert{2}</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>\alert{4}</m></cell>
                        <cell><m>\alert{5}</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p><m>y = \sqrt{x} </m></p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="74"><statement><p>
        <sidebyside width="70%"><image source="images/fig-chap2-rev-74"><description>curve</description></image></sidebyside></p><p>
        <sidebyside><tabular halign="center" left="minor" right="minor" top="minor" bottom="minor">
            <row>
                <cell><m>x</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>0.5</m></cell>
                <cell><m>1</m></cell>
                <cell><m>1.5</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>4</m></cell>
            </row>
            <row>
                <cell><m>y</m></cell>
                <cell><m>4</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>0.5</m></cell>
                <cell><m>\hphantom{000}</m></cell>
            </row>
        </tabular></sidebyside>
    </p></statement>
    </exercise>

    <exercise number="75"><statement><p>
        <sidebyside width="70%"><image source="images/fig-chap2-rev-75"><description>curve</description></image></sidebyside></p><p>
        <sidebyside><tabular halign="center" left="minor" right="minor" top="minor" bottom="minor">
            <row>
                <cell><m>x</m></cell>
                <cell><m>-3</m></cell>
                <cell><m>-2</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>0</m></cell>
                <cell><m>1</m></cell>
                <cell><m>2</m></cell>
            </row>
            <row>
                <cell><m>y</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>-3</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
            </row>
        </tabular></sidebyside>
    </p></statement>
    <answer><p>
        <ol label="a">
            <li><p>
                <tabular halign="center" left="minor" right="minor" top="minor" bottom="minor">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>-3</m></cell>
                        <cell><m>-2</m></cell>
                        <cell><m>\alert{-1}</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>\alert{5}</m></cell>
                        <cell><m>\alert{0}</m></cell>
                        <cell><m>-3</m></cell>
                        <cell><m>\alert{-4}</m></cell>
                        <cell><m>\alert{-3}</m></cell>
                        <cell><m>\alert{0}</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p><m>y = x^2-4 </m></p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="76"><statement><p>
        <sidebyside width="70%"><image source="images/fig-chap2-rev-76"><description>curve</description></image></sidebyside></p>
        <p> </p>
        <p><tabular halign="center" left="minor" right="minor" top="minor" bottom="minor">
            <row>
                <cell><m>x</m></cell>
                <cell><m>-3</m></cell>
                <cell><m>-2</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>0</m></cell>
                <cell><m>1</m></cell>
                <cell><m>\hphantom{000}</m></cell>
            </row>
            <row>
                <cell><m>y</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>8</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>\hphantom{000}</m></cell>
                <cell><m>-7</m></cell>
            </row>
        </tabular>
    </p></statement>
    </exercise>
</exercisegroup>


<exercisegroup cols="2"><introduction><p>Use a graphing calculator to graph each function on the given domain. Adjust <term>Ymin</term> and <term>Ymax</term> until you can determine the range of the function using the <c>TRACE</c> key. Then verify your answer algebraically by evaluating the function. State the domain and corresponding range in interval notation.</p></introduction>

    <exercise number="77"><statement><p>
        <m>f(t)=-t^2+3t</m>; <m>~~-2\le t\le 4</m>
    </p></statement>
    <answer><p>Domain: <m>[-2, 4]</m>; Range: <m>[-10, -4]</m></p></answer>
    </exercise>

    <exercise number="78"><statement><p>
        <m>g(x)=\sqrt{s-2} </m>; <m>~~2\le s\le 6</m>
    </p></statement>
    </exercise>

    <exercise number="79"><statement><p>
        <m>F(x)=\dfrac{1}{x+2} </m>; <m>~~-2\lt x\le 4</m>
    </p></statement>
    <answer><p>Domain: <m>(-2, 4]</m>; Range: <m>\left[\dfrac{1}{6} , \infty\right)</m></p></answer>
    </exercise>

    <exercise number="80"><statement><p>
        <m>H(x)=\dfrac{1}{2-x} </m>; <m>~~-4\le s\lt 2</m>
    </p></statement>
    </exercise>

</exercisegroup>

</exercises>