appendix-b.xml

<?xml version="1.0" encoding="UTF-8" ?>
<!-- <mathbook><book> -->

<appendix xml:id="appendix-b"   xmlns:xi="http://www.w3.org/2001/XInclude">
<title>Using a Graphing Calculator</title>
<introduction>
    <p>
        This appendix provides instructions for TI-84 or TI-83 calculators from Texas Instruments, but most other calculators work similarly.We describe only the basic operations and features of the graphing calculator used in your textbook.
        <figure xml:id="fig-TI-84"><caption></caption><image source="images/fig-TI-84"><description>TI-84</description></image> </figure>
    </p></introduction>
<section xml:id="appendix-Getting-Started"><title>Getting Started</title><introduction></introduction>


<subsection><title>On and Off</title>
<p>
    Press <c>ON</c> to turn <em>on</em> the calculator (see <xref ref="fig-TI-84" text="type-global"/>a). You will see a cursor blinking in the upper left corner of the Home screen. Press <c>2nd</c><c>ON</c> to turn <em>off</em> the calculator.
</p>

</subsection>

<subsection><title>Numbers and Operations</title>
<p>
    The parentheses keys, the Clear key, and the Enter key are shown in <xref ref="fig-TI-84" text="type-global"/>a. Locate the number keys, operation keys, and arrow keys on your calculator, as shown in <xref ref="fig-TI-84" text="type-global"/>b.
</p>
<p>
    We use the <c>-</c> key for subtraction, but we use the <c>(-)</c> key (located next to <c>ENTER</c>) for negative numbers.
</p>
<example>
    <p>
        Compute <m>5 - 8</m>. Press
    </p>
    <sidebyside>
    <p>
        <m>5</m><c> - </c><m>8</m><c>ENTER</c>
    </p>
    <p>
        Ans. <m>-3</m>
    </p>        
    </sidebyside>
</example>
<example>
    <p>
        Compute <m>-5 + 8</m>. Press
    </p>
    <sidebyside>
    <p>
        <c>(-)</c><m>5</m><c> + </c><m>8</m><c>ENTER</c>
    </p>
    <p>
        Ans. <m>3</m>
    </p>        
    </sidebyside>
</example>

<p>
    We press <c>ENTER</c> to tell the calculator to compute.
</p>
<p>
    The calculator has a key for the value of <m>\pi</m>.
</p>
<example>
    <p>
        Compute <m>2\pi</m>. Press
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <m>2</m><c>X</c><c>2nd</c><c> ^ </c><c>ENTER</c><m>~~</m>
        or <m>~~2</m><c>2nd</c><c> ^ </c><c>ENTER</c>
    </p>
    <p>
        Ans. <m>6.283185307</m>
    </p>        
    </sidebyside>
</example>
</subsection>
<subsection><title>Clear and Delete</title>
<p>
    Press <c>DEL</c> to delete the character under the cursor.
</p>
<p>
    Press <c>CLEAR</c> to clear the contents of the current input line.
</p>
<p>
    In the Home screen, press <c>CLEAR</c> <c>CLEAR</c> to clear the entire screen.
</p>
<paragraphs xml:id="troubleshooting"><title>Troubleshooting</title>
    <p>
        <ol label="*1*">
            <li><p>
                If your screen is too light, press <c>2nd</c> <c>↑</c> several times to make it darker. If it is too dark, press <c>2nd</c> <c>↓</c>.
            </p></li>
            <li><p>
                For the features we use in this book, the MODE and FORMAT should be in their default settings. Press <c>MODE</c> to see the menu in Figure B.2a, and <c>2nd</c> <c>ZOOM</c> to see the format menu in <xref ref="fig-GC-settings" text="type-global"/>b. Use the Arrow keys and <c>ENTER</c> to alter the menus to the default settings if necessary. <em>Note</em>: The Set Clock function does not appear on the T1-83.
                <figure xml:id="fig-GC-settings"><caption></caption><image source="images/fig-GC-settings.jpg"  width="75%"><description>GC windows of settings</description></image> </figure>
            </p></li>
        </ol>
    </p>
</paragraphs>
</subsection>
</section>


<section xml:id="appendix-Entering-Expressions"><title>Entering Expressions</title><introduction></introduction>
<subsection><title>Parentheses</title>
<p>
    <term>Order of Operations</term>: The calculator follows the standard order of operations.
</p>
<example>
    <p>
        Compute <m>2+3\cdot4</m>. Press
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <m>2\,</m><c> + </c> <m>\,3\,</m><c> X </c> <m>\,4</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>14</m>
    </p>        
    </sidebyside>
</example>
<example>
    <p>
        Compute <m>(2+3)\cdot4</m>. Press
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <c> ( </c><m>\,2\,</m><c> + </c> <m>\,3\,</m><c> ) </c><c> X </c> <m>\,4</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>20</m>
    </p>        
    </sidebyside>
</example>
<example>
    <p>
        Compute <m>\dfrac{1}{2\cdot 3} </m>. Press
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <m>1 \,\boxed{\div} </m> <c> ( </c><m>\,2\,</m><c> X </c> <m>\,3\,</m><c> ) </c> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>0.1666666667</m>
    </p>        
    </sidebyside>
</example>
<example>
    <p>
        Compute <m>\dfrac{1+3}{2} </m>. Press
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <c> ( </c><m>1 \, </m> <c> + </c> <m>\,3\,</m><c> ) </c> <m>\boxed{ \div } \,2\,</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>2</m>
    </p>        
    </sidebyside>
</example>    
</subsection>
<subsection><title>Exponents and Powers</title>
<p>
    <term>Exponents</term>:  We use the caret key, <c> ^ </c>, to enter exponents or powers.
</p>
<example>
    <p>
        Evaluate <m>2^{10}</m>. 
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <m>2</m> <c> ^ </c> <m>10</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>1024</m>
    </p>        
    </sidebyside>
</example>  
<p>
    <term>Squaring</term>: There is a short-cut key for squaring, <m>\boxed{x^2}</m>.
</p>  
<example>
    <p>
        Evaluate <m>57^{2}</m>. 
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <m>57~\boxed{x^2}\,</m>  <c>ENTER</c>
    </p>
    <p>
        Ans. <m>3249</m>
    </p>        
    </sidebyside>
</example>  
<p>
    <term>Fractional Exponents</term>: Fractional exponents must be enclosed in parentheses!
</p>  
<example>
    <p>
        Evaluate <m>8^{2/3}</m>. 
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <m>8\,</m> <c> ^ </c> <c> ( </c> <m>2  ~ \boxed{\div} \, 3 \,</m> <c> ) </c> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>4</m>
    </p>        
    </sidebyside>
</example> 
</subsection>

<subsection><title>Roots</title>
<p>
    <term>Square Roots</term>: We access the square root by pressing <c>2nd</c> <m>\boxed{x^2} </m>, and the display shows <m>\sqrt{}(</m>. The calculator automatically gives an open parenthesis for the square root, but not a close parenthesis.
</p>
<example>
    <p>
        Evaluate <m>\sqrt{2} </m>. 
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <c>2nd</c> <m>\boxed{x^2} \,2\,</m> <c> ) </c> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>1.414213562</m>
    </p>        
    </sidebyside>
</example> 
<example>
    <p>
        Evaluate <m>\sqrt{9+16} </m>. 
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <c>2nd</c> <m>\boxed{x^2} \,9+16\,</m> <c> ) </c> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>5</m>
    </p>        
    </sidebyside>
</example> 
<p>
    In the next example, note that we must enter <c>)</c> at the end of the radicand to tell the calculator where the radical ends.
</p>
<example>
    <p>
        Evaluate <m>\sqrt{9}+16 </m>. 
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <c>2nd</c> <m>\boxed{x^2} \,9</m> <c> ) </c> <m>{}+{}16\,</m>  <c>ENTER</c>
    </p>
    <p>
        Ans. <m>19</m>
    </p>        
    </sidebyside>
</example> 
<p>
    <term>Cube Roots</term>: For cube roots, we press <c>MATH</c> to open the Math menu and press <m>4</m> (see <xref ref="fig-GC-settings2" text="type-global"/>).
    <figure xml:id="fig-GC-settings2"><caption></caption><image source="images/fig-GC-settings2.jpg"  width="70%"><description>two GC settings</description></image> </figure>
</p>
<example>
    <p>
        Compute <m>\sqrt[3]{1728} </m>. 
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <c>MATH</c> <m>~4~</m> <m>\, 1728\,</m> <c>)</c> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>12</m>
    </p>        
    </sidebyside>
</example> 
<p>
    For evaluating cube roots and square roots, <c>)</c> can be omitted if there are no operations following the radical.
</p>
<p>
    <term>Other Roots</term>: For <m>n</m>th roots, we press <c>MATH</c> to open the Math menu and press <m>5</m> (see <xref ref="fig-GC-settings2" text="type-global"/>a). The calculator symbol for <m>n</m>th roots, <m>\sqrt[x]{~} </m>, does not include an open parenthesis,<c>(</c>. If the radicand includes an operation, we must enclose it in parentheses.
</p>
<example>
    <p>
        Compute <m>\sqrt[10]{2\cdot 512} </m>. 
    </p>
    <sidebyside widths="60% 35%">
    <p>
        <m>10\,</m><c>MATH</c> <m>~5~</m> <c>(</c> <m>2</m> <c> x </c> <m>512</m> <c>)</c> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>2</m>
    </p>        
    </sidebyside>
</example> 
<p>
    Notice that we enter the index 10 <em>before</em> the radical symbol.
</p>
</subsection>


<subsection><title>Absolute Value</title>
<p>
    TI calculators use <m>abs (x)</m> instead of <m>\abs{x}</m> to denote the absolute value of <m>x</m>. The absolute value function is the first entry in the MATH NUM menu (see <xref ref="fig-GC-settings3" text="type-global"/>). The calculator gives <c>(</c> for the absolute value function, but not <c>)</c>.
    <figure xml:id="fig-GC-settings3"><caption></caption><image source="images/fig-GC-settings3.jpg"  width="40%"><description>GC Math NUM menu</description></image> </figure>
</p>
<example>
    <p>
        Evaluate <m>\dfrac{\abs{21\cdot 54 - 81}}{-9} </m>. 
    </p>
    <sidebyside widths="65% 30%">
    <p>
        <c>MATH</c> <c>→</c> <c>ENTER</c> <m>21</m> <c>X</c> <m>54</m> <c> -</c> <m>81</m> <c> )</c> <m>\,\boxed{\div} </m> <c>(-)</c> <m>9</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>-117</m>
    </p>        
    </sidebyside>
</example> 
</subsection>

<subsection><title>Scientific Notation</title>
<p>
    The TI calculators display numbers in scientific notation when the numbers use too many digits to display.
</p>
<example>
    <p>
        Compute <m>123,456,789^2 </m>. Enter
    </p>
    <sidebyside widths="65% 30%">
    <p>
        <m>123456789 ~ \boxed{x^2}</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>1.524157875 \text{ E }16</m>
    </p>        
    </sidebyside>
</example> 
<p>
    This is how the calculator displays the number <m>1.524157875 \times 10^{16}</m>. Notice that the power <m>10^{16}</m> is displayed as <m>\text{ E }16</m>.
</p>
<p>
    To enter a number in scientific form, we use the key labeled <term>EE</term>, or <c>2nd</c> <c> ,</c>.
</p>
<example>
    <p>
        To enter <m>3.26 \times 10^{18}</m>, use the keying sequence
    </p>
    <sidebyside widths="65% 30%">
    <p>
        <m>3.26</m> <c>2nd</c> <c> ,</c> <c>(-)</c> <m>18</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>3.26 \text{ E}</m> <m>-18</m>
    </p>        
    </sidebyside>
</example> 
<paragraphs><title>Troubleshooting</title>
<p>
    <figure xml:id="fig-GC-syntax"><caption></caption><image source="images/fig-GC-syntax.jpg"  width="25%"><description>GC syntax error screen</description></image> </figure>
    If your calculator gives you an error message like this, you may have made one of the following common mistakes:
    <ol label="*1*">
        <li><p>
            Using the negative key, <c>(-)</c>, when you wanted the subtraction key, <c> -</c>, or vice versa.
        </p></li>
        <li><p>
            Omitting a <c>(</c> or <c>)</c>. Each <c>(</c> should have a matching <c>)</c>.
        </p></li>
    </ol>
    Press <m>2</m> to <term>Go to</term> the error, and see <xref ref="appendix-Editing-Expressions"> Editing Expressions</xref> below.
</p></paragraphs>
</subsection>
</section>

<!--


    -->

<section xml:id="appendix-Editing-Expressions"><title>Editing Expressions</title><introduction></introduction>
<subsection><title>Overwriting</title>
<p>
    We can edit an expression without starting again. If we place the cursor over a symbol and press a new key, the new symbol replaces (overwrites) the old one.
</p>
<example>
    <p>
        Correct the error in the following keystrokes for <m>120 – 36</m>:
        <me>120 \, \boxed{(-)} \, 36\, \boxed{\text{ENTER}} </me>
    </p>
    <p>
        The calculator gives an error message (See <xref ref="fig-GC-syntax" text="type-global"/>.) Select "2:Goto", and a blinking cursor appears over the error. Press <c> -</c> to replace the negative symbol by the subtraction symbol.
</p></example> 
</subsection>

<subsection><title>Recalling an Entry</title>
<p>
    We can recall a previous entry by pressing <c>2nd</c> <c>ENTER</c>.
</p>
<example>
    <p>
        Evaluate <m>\sqrt{3}+\sqrt{2}~~ </m> and <m>~~\sqrt{3}-\sqrt{2} </m>. First evaluate <m>\sqrt{3}+\sqrt{2} </m>:
    </p>
   <sidebyside widths="65% 30%">
    <p>
        <c>2nd</c> <m>\boxed{x^2} ~ 3\,</m> <c>)</c> <c>+</c> <c>2nd</c> <m>\boxed{x^2}  ~2\,</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>3.14626437</m>
    </p>
    </sidebyside>
    <p>
        Now press <c>2nd</c> <c>ENTER</c> to recall the last entry, and use the left arrow key <c>←</c> to position the cursor over <m>+</m>. Press <c>-</c> to change to <m>{}-{}</m>, then press <c>ENTER</c>. Your screen should look like <xref ref="fig-GC-sum-of-roots" text="type-global"/>.
        <figure xml:id="fig-GC-sum-of-roots"><caption></caption><image source="images/fig-GC-sum-of-roots.jpg"  width="25%"><description>GC with sum and difference of roots</description></image> </figure>
</p></example> 
</subsection>

<subsection><title>Inserting a Character</title>
<p>
    To insert a new character <em>before</em> a symbol, position the cursor over that symbol and press <c>2nd</c> <c>DEL</c> to get the <term>INS</term> (insert) command.
</p>
<example>
    <p>
        Evaluate <m>\sqrt{3}-5\sqrt{2} </m> by editing the example above.
    </p>
    <p>
        Press  <c>2nd</c> <c>ENTER</c>  to recall the last entry, and use the left arrow key <c>←</c> to position the cursor over the second <m>\sqrt{\,}</m> from left to right. Press <c>2nd</c> <c>DEL</c>  <m>5</m> to insert 5 <em>before</em> the <m>\sqrt{\,}</m> symbol, then press <c>ENTER</c>. Your screen should look like <xref ref="fig-GC-sum-of-roots2" text="type-global"/>.
        <figure xml:id="fig-GC-sum-of-roots2"><caption></caption><image source="images/fig-GC-sum-of-roots2.jpg"  width="25%"><description>GC with sum of roots</description></image> </figure>
    </p>
</example>
</subsection>

<subsection><title>Recalling an Answer</title>
<p>
    We often want to use the result from a previous calculation in a new calculation, without having to type in the number. We use the <term>ANS</term> key, <c>2nd</c> <c>(-)</c>, to recall the answer to the last calculation.
</p>
<example>
    <p>
        <ol label="a">
            <li><p>
                Evaluate <m>\sqrt{5}-1 </m>
   <sidebyside widths="65% 30%">
    <p>
        <c>2nd</c> <m>\boxed{x^2} ~ 5\,</m> <c>)</c> <c>-</c>  <m>1 \,</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>1.236067977</m>
    </p>
    </sidebyside>
            </p></li>
            <li><p>
                Evaluate <m>x^2 + 2x + 1</m> for <m>x = \sqrt{5}-1 </m>. Because <m>x</m> is the last answer the calculator computed, we enter
   <sidebyside widths="65% 30%">
    <p>
        <c>2nd</c> <c>(-)</c> <m>\boxed{x^2}\,</m> <c>+</c> <m>2\,</m> <c>2nd</c> <c>(-)</c> <c>+</c>  <m>1 \,</m> <c>ENTER</c>
    </p>
    <p>
        Ans. <m>5</m>
    </p>
    </sidebyside>
            Your screen should look like <xref ref="fig-GC-sum-of-roots3" text="type-global"/>.
        <figure xml:id="fig-GC-sum-of-roots3"><caption></caption><image source="images/fig-GC-sum-of-roots3.jpg"  width="25%"><description>GC roots minus 1</description></image> </figure>
            </p></li>
        </ol>
    </p>
</example>
</subsection>
</section>

<!-- 


 -->
<section xml:id="appendix-Graphing-an-Equation"><title>Graphing an Equation</title><introduction>
<p>
    We can graph equations written in the form <m>y = </m> (expression in x). The graphing keys are located on the top row of the keypad. There are two steps to graphing an equation:
    <ol label="*1*">
        <li><p>
            Entering the equation
        </p></li>
        <li><p>
            Setting the graphing window
        </p></li>
    </ol>
</p></introduction>
<subsection><title>Standard Window</title>
<p>
    The standard window displays values from <m>-10</m> to <m>10</m> on both axes.
</p>
<example>
    <p>
        <ol label="*1*">
            <li><p>
                Press <c>Y=</c> and enter <m>2X-5</m> after <m>Y_1=</m> by keying in
                <md>
                    <mrow>2~ \boxed{X, T, \theta, n} ~ \boxed{{}-{}} ~ 5 \amp\amp\amp\text{Use the } \boxed{X, T, \theta, n} ~ \text{ to enter }X.</mrow>
                </md>
            </p></li>
            <li><p>
                Press  <c>ZOOM</c> <m>6</m> to set the standard window, and the graph will appear (see <xref ref="fig-GC-graphing-windows" text="type-global"/>).
                <figure xml:id="fig-GC-graphing-windows"><caption></caption><image source="images/fig-GC-graphing-windows.jpg"><description>GC graphing screens</description></image> </figure>
            </p></li>
        </ol>
        You can press <c>2nd</c> <c>WINDOW</c> to see the settings for the standard window. <m>Xscl = 1</m> means that the tick marks on the <m>x</m>-axis are spaced <m>1</m> unit apart.
    </p>
    <p>
        Press <c>2nd</c> <c>MODE</c> to Quit the graph and return to the Home screen, where we enter computations. From the Home screen, press <c>GRAPH</c> to return to the graph.
    </p>
</example>
</subsection>


<subsection><title>Tracing</title>
<p>
    The calculator can display the coordinates of selected points on the graph. Press the <c>TRACE</c> key to see a "bug" blinking on the graph. The coordinates of the bug are displayed at the bottom of the screen. Use the left and right arrow keys to move the bug along the graph, as shown in <xref ref="fig-GC-tracing" text="type-global"/>. Note that the <term>Trace</term> feature does not show every point on the graph!
    <figure xml:id="fig-GC-tracing"><image source="images/fig-GC-tracing.jpg"><description>GC tracing bug</description></image> <caption></caption> </figure>
</p>

<example>
    <p>
        Use the <term>Trace</term> to find the point on the graph with <m>x=-3</m>. Press
        <me>\boxed{\text{TRACE}} \, \boxed{(-)} \, 3 \, \boxed{\text{ENTER}} </me> 
The bug is off the bottom of the screen, but the coordinates are still shown.
    </p>
</example>
</subsection>


<subsection><title>Multiple Graphs</title>
<p>
    You can enter more than one graph at a time. Press <c>↓</c> to enter a second equation at <m>Y_2 =</m>, at <m>Y_3 =</m>, and so on. When Tracing, press the <c>↓</c>  and <c>↑</c> keys to move from one graph to another.
</p>
<p>
    To turn off a graph without deleting its equation, press and move the cursor over the <m>=</m> sign in the equation. Press <c>ENTER</c> to deactivate that equation. (When you move the cursor away, the <m>=</m> sign is no longer highlighted.) To reactivate the equation, move the cursor back over the <m>=</m> sign and press <c>ENTER</c> again.
</p>
</subsection>


<subsection><title>Setting the Window</title>
<p>
    Of course, the standard window is not suitable for every graph.
</p>
<example>
    <p>
        Graph <m>y= 0.01x^2- 50</m> in the window
        <md>
            <mrow>
                \text{Xmin} \amp = -100 \amp\amp \text{Xmax} = 100
            </mrow>
            <mrow>
                \text{Ymin} \amp = -60 \amp\amp \text{Ymax} = 50
            </mrow>
        </md>
        <ol label="*1*">
            <li><p>
                Press <c>Y=</c> and enter <m>0.01X^2-50</m> by keying in
                <me>0.01 ~ \boxed{X,T,\theta,n}~\boxed{x^2}~\boxed{{}-{}} 50 \hphantom{blank} \text{Use the }  \boxed{X,T,\theta,n}\text{ key to enter} X.</me>
            </p></li>
            <li><p>
                Press <c>WINDOW</c> and enter the settings as shown in <xref ref="fig-GC-window-settings" text="type-global"/>. Use the up and down arrow keys to move from line to line. Then press <c>GRAPH</c>.
                <figure xml:id="fig-GC-window-settings"><caption></caption><image source="images/fig-GC-window-settings.jpg"  width="30%"><description>GC window settings screen</description></image> </figure>
            </p></li>
        </ol>
    </p>
</example>
</subsection>

<subsection><title>Intersect Feature</title>
<p>
    We can use the calculator to find the intersection point of two graphs:
    <ol label="*1*">
        <li><p>
            Enter the equations for the two graphs in the <c>Y=</c> menu.
        </p></li>
        <li><p>
            Choose window settings so that the intersection point is visible in the window.
        </p></li>
        <li><p>
            Press <c>2nd</c> <c>TRACE</c> <m>5</m> to activate the intersect feacture.
        </p></li>
        <li><p>
            Use the left and right arrow keys to position the bug near the intersection point.
        </p></li>
        <li><p>
            Respond to each of the calculator’s questions, First curve?, Second curve?, and Guess? by pressing <c>ENTER</c>. The coordinates of the intersection point are then displayed at the bottom of the screen.
        </p></li>
    </ol>
    <xref ref="fig-GC-intersect" text="type-global"/> shows one of the intersection points of <m>y = 0.01x^2 - 50</m> and <m>y = -0.5x</m>.
    <figure xml:id="fig-GC-intersect"><caption></caption><image source="images/fig-GC-intersect.jpg"  width="40%"><description>GC intersection of graphs</description></image> </figure>
</p>
</subsection>

<subsection><title>Other Windows</title>
<p>
    <ol label="*1*">
        <li><p>
            The <term>ZDecimal</term> (Zoom Decimal) window, accessed by pressing <c>ZOOM</c> <m>4</m>, shows <m>x</m>-values from <m>-4.7</m> to <m>4.7</m> only, but the <term>Trace</term> feature shows "nice" <m>x</m>-values in increments of <m>0.1</m>.
        </p></li>
        <li><p>
            The <term>ZInteger</term> (Zoom Integer) window shows nice <m>x</m>-values in increments of <m>1</m> unit. Access the <term>ZInteger</term> window as follows: Press <c>ZOOM</c> <m>8</m>, move the bug with the arrow keys to the center of your new window, and press <c>ENTER</c>.
        </p></li>
        <li><p>
            The <term>ZSquare</term> window, accessed by pressing <c>ZOOM</c> <m>5</m>, makes the tick marks on both axes have the same size. In this window, squares look like squares, circles look like circles, and all angles appear true.
        </p></li>
        <li><p>
            <term>"Friendly" Windows</term>: If the difference between Xmin and Xmax is a multiple of <m>94</m>, the <term>Trace</term> feature gives nice values for <m>x</m>. A useful example of a friendly window is <m>Xmin=-9.4</m>, <m>Xmax= 9.4</m>.
        </p></li>
    </ol>
</p>
<paragraphs><title>Troubleshooting</title>
<p>
    <ol label="*1*">
        <li><p>
            If the graph is not visible, you may need to adjust your window. Or, the equation may not be activated. Press <c>Y=</c> and check to see if the <m>=</m>sign is highlighted.
        </p></li>
        <li><p>
            If you get a range error, ERR: WINDOW RANGE, quit the message and press <c>WINDOW</c>. Alter the window settings so that Xmin is smaller than Xmax and so that Ymin is smaller than Ymax.
        </p></li>
        <li><p>
            If you press and get an unfamiliar window, or if the axes are not visible in the ZStandard window, you may need to return the <term>Mode</term> or <term>Format</term> menus to their default settings. See <xref ref="troubleshooting" text="global">Troubleshooting</xref> in <xref ref="appendix-Getting-Started" text="type-global"/>.
        </p></li>
        <li><p>
            If you get a dimension error, <term>ERR: INVALID DIM</term>, you may have a StatPlot turned on. Press <c>2nd</c> <c>Y=</c> <m>4</m> <c>ENTER</c> to turn off the StatPlots.
        </p></li>
        <li><p>
            If the bug does not move along the curve, <c>TRACE</c> may not be activated. Press <c>TRACE</c> and then the left or right arrow key.
        </p></li>
        <li><p>
            If you get the error, <term>ERR: INVALID</term>, you have probably entered a value of <m>x</m> that is outside the window. Adjust the window settings accordingly.
        </p></li>
        <li><p>
            If the <m>x</m>-axis or <m>y</m>-axis is too thick, the tick marks are too close together. Press <c>WINDOW</c> and make Xscl or Yscl larger. Set <m>Xscl=0</m> or <m>Yscl =0</m> to remove the tick marks.
        </p></li>
        <li><p>
            If you get <term>ERR: NO SIGN CHNG</term> when using the intersect feature, the calculator did not find any intersection point within the current window. Alter the window settings so that the two curves meet within the window. If the two curves are tangent, the calculator may simply fail to find the point of intersection.
        </p></li>
    </ol>
</p>
</paragraphs>
</subsection>

</section>

<!-- 

 -->

<section xml:id="appendix-Making-a-Table"><title>Making a Table</title><introduction>
<p>
    The table feature gives us a convenient tool for evaluating expressions. There are two steps to making a table:
    <ol label="*1*">
        <li><p>
            Entering the equation
        </p></li>
        <li><p>
            Setting the Table features
        </p></li>
    </ol>
</p></introduction>
<subsection><title>Using the Auto Option</title>
<p>
    If we want a table with evenly spaced <m>x</m>-values, we use the Automatic setting.
    <ol label="*1*">
        <li><p>
            Press <c>Y=</c>, clear any previous entries, and enter the expression or expressions you want to evaluate.
        </p></li>
        <li><p>
            Press <c>2nd</c> <c>WINDOW</c> (<term>TBLSET</term>) to access the Table Setup menu. Enter the first <m>x</m>-value after <term>TblStart</term><m>=</m>, and the <m>x</m>-increment after <m>\Delta Tbl=</m>. Highlight <term>Auto</term> for both the Independent and Dependent variables.
        </p></li>
        <li><p>
            Finally, press <c>2nd</c> <c>GRAPH</c> (<term>TABLE</term>) to see the table. You can use the arrows to scroll up and down the table. <xref ref="fig-GC-table-setup" text="type-global"/> shows the Table Setup and the resulting table for <m>y = 5 - x^3</m>.
            <figure xml:id="fig-GC-table-setup"><caption></caption><image source="images/fig-GC-table-setup.jpg"  width="70%"><description>GC table setup and table</description></image> </figure>
        </p></li>
    </ol>
</p>
</subsection>


<subsection><title>Using the Ask Option</title>
<p>
    If we want to choose specific <m>x</m>-values for the table, we proceed as above but choose <term>Ask</term> instead of <term>Auto</term> for the Independent variable. Press <c>2nd</c> <c>GRAPH</c> to see the table, then enter the <m>x</m>-values, pressing <c>ENTER</c> after each one.
</p>
<paragraphs><title>Troubleshooting</title>
<p>
    <ol label="*1*">
        <li><p>
            If the table shows <term>ERROR</term> for a <m>y</m>-value, the expression you entered is undefined at the corresponding <m>x</m>-value.
        </p></li>
        <li><p>
            If the table shows only <m>x</m>-values, no equation is activated. Press <c>Y=</c> to enter or activate an equation.
        </p></li>
    </ol>
</p>
</paragraphs>
</subsection>

</section>
<!-- 


 -->

<section xml:id="appendix-Regression"><title>Regression</title><introduction>
<p>
    We use the statistics features to plot data and calculate regression equations. Press <c>STAT</c> to see the Statistics menus. We will use only the first two, <term>EDIT</term> and <term>CALC</term>.
</p></introduction>

<subsection xml:id="scatterplot"><title>Making a Scatterplot</title>
<p>
    <ol label="*1*">
        <li><p>
            Press <c>STAT</c> <c>ENTER</c> to access the list editor.
        </p></li>
        <li><p>
            Enter the <m>x</m>-coordinates of the data points under L1 and the <m>y</m>-coordinates in L2. An example is shown in <xref ref="fig-GC-scatterplot" text="type-global"/>a. (If there is a previous list under L1 or L2, move the cursor up to L1 or L2 and press <c>CLEAR</c> <c>ENTER</c>.)
            <figure xml:id="fig-GC-scatterplot"><caption></caption><image source="images/fig-GC-scatterplot.jpg"><description>GC screens for scatterplot</description></image> </figure>
        </p></li>
        <li><p>
            Access the STAT PLOT menu by pressing <c>2nd</c> <c>Y=</c>, select and turn on Plot1 by pressing <c>ENTER</c> <c>ENTER</c>, and set the menu options as shown in <xref ref="fig-GC-scatterplot" text="type-global"/>b.
        </p></li>
        <li><p>
            Clear out any old equations from the <c>Y=</c> menu, then press <c>ZOOM</c> <m>9</m> (ZoomStat) to see the scatterplot.
        </p></li>
    </ol>
    <em>Note</em>: You can use any of the lists L1–L6 to store the data. Change Xlist and Ylist to reflect the appropriate lists.
</p>

<warning>
    <p>
        When you are through with the scatterplot, press <c>Y=</c> <c>↑</c> <c>ENTER</c> to turn off Plot1 (or press <c>2nd</c> <c>Y=</c> <m>4</m> to turn off all the StatPlots). If you neglect to do this, you will continue to see the scatterplot even after you graph a new equation.
    </p>
</warning>
</subsection>


<subsection xml:id="regression-equation"><title>Finding a Regression Equation</title>
<p>
    <ol label="*1*">
        <li><p>
            Enter the data as in steps 1 and 2 of Making a Scatterplot.
        </p></li>
        <li><p>
            Press <c>STAT</c> <c>→</c> to open the Calculate menu, and select the type of regression equation you want.
        </p></li>
        <li><p>
            Press <c>ENTER</c> and the calculator will display the parameters of the regression equation. See the example in <xref ref="fig-GC-regression-line" text="type-global"/>. (You may also see information about <m>r</m> and <m>r^2</m>.)
            <figure xml:id="fig-GC-regression-line"><caption></caption><image source="images/fig-GC-regression-line.jpg"><description>GC screens for regression line</description></image> </figure>
        </p></li>
    </ol>
    Note: If you do not use L1 and L2 to store the data, enter the appropriate lists, separated by a comma, after the regression command.
</p>
</subsection>


<subsection><title>Graphing the Regression Equation</title>
<p>
    If you would like to graph the regression equation on top of the scatterplot, first follow the steps in <xref ref="scatterplot" text="global">Making a Scatterplot</xref> and <xref ref="regression-equation" text="global">Finding a Regression Equation</xref> above.
    <ol label="*1*">
        <li><p>
            Press <c>Y=</c> and clear out any old equations.
        </p></li>
        <li><p>
            Position the cursor after <m>Y_1 =</m>.
        </p></li>
        <li><p>
            Press <c>VARS</c> <m>5</m> <c>→</c> <c>→</c> <c>ENTER</c> to copy the regression equation.
        </p></li>
        <li><p>
            Press <c>GRAPH</c> to see graph of the regression equation and the scatterplot.
        </p></li>
    </ol>
</p>
</subsection>
</section>
<!-- 


 -->

<section xml:id="appendix-Function-Notation-and-Transformation-of-Graphs"><title>Function Notation and Transformation of Graphs</title><introduction></introduction>
<subsection><title>Function Notation</title>
<p>
    The calculator uses <m>Y_1 (X)</m>, <m>Y_2 (X)</m>, and so on, instead of <m>f (x)</m>, <m>g(x)</m>, and so on, for function notation.
</p>

<example>
    <p>
        Evaluate <m>f (x) = x^2 + 6x + 9</m> for <m>x = 3</m>.
        <ol label="*1*">
            <li><p>
                Set <m>Y_1 = X^2 + 6X + 9</m>, and quit (<c>2nd</c> <c>MODE</c>) to the Home screen.
            </p></li>
            <li><p>
                To evaluate this function for <m>X = 3</m>, press</p>
                <p><c>VARS</c> <c>→</c> <c>ENTER</c> <c>ENTER</c> <c>(</c> <m>3</m> <c>)</c> <c>ENTER</c></p>
                <p>See <xref ref="fig-GC-evaluate-function" text="type-global"/>.
<figure xml:id="fig-GC-evaluate-function"><caption></caption><image source="images/fig-GC-evaluate-function.jpg"  width="60%"><description>GC evaluating a function</description></image> </figure>
            </p></li>
        </ol>
    </p>
</example>
</subsection>

<subsection><title>Transformation of Graphs</title><introduction>
<p>
    We can use function notation to facilitate graphing transformations. In the examples below, we use <m>f (x) = x^2</m>.
</p></introduction>
<subsubsection><title>Translations</title>
<example>
    <p>
        Compare the graphs of <m>y = f (x) - 8</m> and <m>y = f (x - 8)</m> with that of <m>y = f (x)</m>.
    </p>
    <p>
        Define <m>Y_1 = X^2</m> and <m>Y_2 =Y_1(X) - 8</m> . Press <c>ZOOM</c> <m>6</m> to see the graphs (<xref ref="fig-GC-vertical-shift" text="type-global"/>).
    <figure xml:id="fig-GC-vertical-shift"><caption></caption><image source="images/fig-GC-vertical-shift.jpg"  width="50%"><description>GC vertical shift of parabola</description></image> </figure>
    </p>
    <p>
        Define <m>Y_1 = X^2</m> and <m>Y_2 =Y_1(X - 8)</m>. Press <c>ZOOM</c> <m>6</m> to see the graphs (<xref ref="fig-GC-horizontal-shift" text="type-global"/>).
    <figure xml:id="fig-GC-horizontal-shift"><caption></caption><image source="images/fig-GC-horizontal-shift.jpg"  width="50%"><description>GC horizontal shift of parabola</description></image> </figure>
    </p>
</example>
</subsubsection>
<subsubsection><title>Vertical Scalings and Reflections</title>
<p>
    Compare the graph of <m>y = \frac{-1}{2} f (x)</m> with that of <m>y = f (x)</m>.
</p>
<p>
    Define <m>Y_1 = X^2</m> and <m>Y_2 = -1/2*Y_1(X)</m>. Press to see the graphs (<xref ref="fig-GC-vertical-flip" text="type-global"/>).
        <figure xml:id="fig-GC-vertical-flip"><caption></caption><image source="images/fig-GC-vertical-flip.jpg"  width="50%"><description>GC vertical reflection of parabola</description></image> </figure>

</p>
</subsubsection>
</subsection>

</section>

</appendix>


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