Now You Try

<p>Aaron did his homework at school with a graphing calculator. He determined that the equation of the line of best fit for some data was <code class='latex inline'>y=2.63x-1.29</code>. Once he got home, he realized he had mixed up the independent and dependent variables. Write the correct equation for the relation in the form <code class='latex inline'>y=mx+b</code>.</p>

<img src="/qimages/43369" /><p>MATHEMATICAL CONNECTIONS Rewrite each</p><p>geometry formula using function notation. Evaluate each function when <code class='latex inline'>\displaystyle r=5 </code> feet. Then explain the meaning of the result.</p><p>a. Diameter, <code class='latex inline'>\displaystyle d=2 r </code></p><p>b. Area, <code class='latex inline'>\displaystyle A=\pi r^{2} </code></p><p>c. Circumference, <code class='latex inline'>\displaystyle C=2 \pi r </code></p>

<p>Mr. Martinez is a sales representative for an agricultural supply company. He receives a salary and monthly commission. He also receives a bonus each time he reaches a sales goal.</p><p>Write a verbal expression that describes how much Mr. Martinez earns in a year if he receives four equal bonuses.</p>

<p>Erin joins a CD club. The first 10 CDs are free, but after that she pays <code class='latex inline'>\$15.95</code> for each CD she orders.</p>
<ul>
<li>How much would she pay for 15 CDs?</li>
</ul>

<p>John was bringing a message to the principal's office when the principal intercepted him and took the message. When a graph passes through the <code class='latex inline'>\displaystyle y </code> -axis, it has a y-intercept. What do you think a <code class='latex inline'>\displaystyle y </code> -intercept of a graph represents?</p>

<p>Mr. Martinez is a sales representative for an agricultural supply company. He receives a salary and monthly commission. He also receives a bonus each time he reaches a sales goal.</p><p>Suppose Mr. Martinezâ€™s annual salary is $42,000 and his average commission is $825 each month. If he receives four bonuses of $750 each, how much does he earn in a year?</p>

<p>Determine the function that describe the following function rules. Show your work.</p>
<ul>
<li>The sum of the input and output is 5.</li>
</ul>

<p>The circumference, <code class='latex inline'>C</code>, in kilometres, of the tropical storm in question 5 can be modelled by the function <code class='latex inline'>C(r) =2\pi r</code>.</p><p><strong>a)</strong> Graph <code class='latex inline'>C(r)</code> for <code class='latex inline'>r\in [0, 10]</code></p><p><strong>b)</strong> State the domain and range.</p><p><strong>c)</strong> Describe the similarities and differences between the graph of <code class='latex inline'>C(r)</code> and the graph of <code class='latex inline'>y = x</code>.</p>

<p>A company rents cars for <code class='latex inline'>\$50</code> per day plus <code class='latex inline'>\$0.15/km</code>.</p><p><strong>(a)</strong> Express the daily rental cost as a function of the number of kilometres travelled.</p><p><strong>(b)</strong> Determine the rental cost if you drive 472 km in one day.</p><p><strong>(c)</strong> Determine how far you can drive in a day for $80. </p>

<p>Create a linear function machine and two points that are generated by the machine. Trade points with a classmate to determine the function that generated the points.</p>

<p>Martin wants to build an additional closet in a corner of his bedroom. Because the closet will be in a corner, only two new walls need to be built. The total length of the two new walls must be 12 m. Martin wants the length of the closet to be twice as long as the width, as shown in the diagram. Show your work.</p><p> Graph <code class='latex inline'>y = f(l)</code>.</p>

<p>Shopping You are buying orange juice for <code class='latex inline'>\displaystyle \$ 4.50 </code> per container and have a gift card worth <code class='latex inline'>\displaystyle \$ 7 . </code> The function <code class='latex inline'>\displaystyle f(x)=4.50 x-7 </code> represents your total cost <code class='latex inline'>\displaystyle f(x) </code> if you buy <code class='latex inline'>\displaystyle x </code> containers of orange juice and use the gift card. How much do you pay to buy 4 containers of orange juice?</p>

<img src="/qimages/43366" /><p>PROBLEM SOLVING The function <code class='latex inline'>\displaystyle C(x)=25 x+50 </code> represents the & Hours & Cost \cline { 1 - 3 } labor cost (in dollars) for Certified & 2 & <code class='latex inline'>\displaystyle \$ 130 </code> Remodeling to build a deck, where & 4 & <code class='latex inline'>\displaystyle \$ 160 </code> <code class='latex inline'>\displaystyle x </code> is the number of hours of labor. & 6 & <code class='latex inline'>\displaystyle \$ 190 </code> The table shows sample labor costs & & from its main competitor, Master & & Remodeling. The deck is estimated to take 8 hours of labor. Which company would you hire? Explain.</p>

<p>Erin joins a CD club. The first 10 CDs are free, but after that she pays <code class='latex inline'>\$15.95</code> for each CD she orders.</p><p>It can be modelled by <code class='latex inline'>
\displaystyle
Cost = 15.95x - 159.5
</code></p>
<ul>
<li>Erin receives her first order of CDs with a bill for <code class='latex inline'>\$31.90</code>. Create and solve an equation to determine how many she ordered.</li>
</ul>

<p>Think About a Plan In a factory, a certain machine needs 10 min to warm up. It takes 15 min for the machine to run a cycle. The machine can operate for as long as <code class='latex inline'>\displaystyle 6 \mathrm{~h} </code> per day including warm-up time. Draw a graph showing the total time the machine operates during 1 day as a function of the number of cycles it runs.</p>
<ul>
<li><p>What domain and range are reasonable?</p></li>
<li><p>Is the function a linear function?</p></li>
</ul>

<p>You earn <code class='latex inline'>\displaystyle \$ 10 </code> for each hour you work at a canoe rental shop. Write an expression for your salary for working the number of hours <code class='latex inline'>\displaystyle h </code>. Make a table to find how much you earn for working <code class='latex inline'>\displaystyle 10 \mathrm{~h}, 20 \mathrm{~h}, 30 \mathrm{~h} </code>, and <code class='latex inline'>\displaystyle 40 \mathrm{~h} </code>.</p>

<p>Without graphing, tell whether the slope of a line that models each linear relationship is positive, negative, zero, or undefined. Then find the slope.</p><p>A student earns a 98 on a test for answering one question incorrectly and earns a 90 for answering five questions incorrectly.</p>

<p>The function <code class='latex inline'>s(d)=0.159+0.118d</code> relates the slope, <code class='latex inline'>s</code>, of a beach to the average diameter, <code class='latex inline'>d</code>, in millimetres, of the sand particles on the beach. Which beach has a steeper slope: beach <code class='latex inline'>A</code>, which has very fine sand with <code class='latex inline'>d=0.0625</code>, or beach <code class='latex inline'>B</code>, which has very coarse sand with <code class='latex inline'>d=1?</code> Justify your decision. </p>

<p>You and some friends are going to a museum. Each ticket costs $4.50.</p><p>a. If <code class='latex inline'> n </code> is the number of tickets purchased, write an expression that gives the total
cost of buying <code class='latex inline'> n </code> tickets.</p><p>b. Suppose the total cost for <code class='latex inline'> n </code> tickets is <code class='latex inline'> \$ 36 </code> . What is the total cost if one more ticket
is purchased?</p>

<p>Describe and correct the error in the statement about the relation shown in the table. </p><p><code class='latex inline'>\displaystyle
\begin{array}{|l|l|l|l|l|l|}
\hline Input, \boldsymbol{x} & 1 & 2 & 3 & 4 & 5 \\
\hline Output, \boldsymbol{y} & 6 & 7 & 8 & 6 & 9 \\
\hline
\end{array}
</code></p><p>The relation is a function. The</p><p>range is <code class='latex inline'>\displaystyle 1,2,3,4 </code>, and <code class='latex inline'>\displaystyle 5 . </code></p>

<p>Martin wants to build an additional closet in a corner of his bedroom. Because the closet will be in a corner, only two new walls need to be built. The total length of the two new walls must be <code class='latex inline'>12</code> m. Martin wants the length of the closet to be twice as long as the width, as shown in the diagram. </p><p>What is <code class='latex inline'>l</code> as a function of <code class='latex inline'>w</code>? Show your work.</p>

<p>Without graphing, tell whether the slope of a line that models each linear relationship is positive, negative, zero, or undefined. Then find the slope.</p><p>The length of a bus route is <code class='latex inline'>\displaystyle 4 \mathrm{mi} </code> long on the sixth day and <code class='latex inline'>\displaystyle 4 \mathrm{mi} </code> long on the seventeenth day.</p>

<img src="/qimages/43242" /><p>MULTIPLE REPRESENTATIONS The balance</p><p><code class='latex inline'>\displaystyle y </code> (in dollars) of your savings account is a function of the month <code class='latex inline'>\displaystyle x </code>.</p><p>Month, <code class='latex inline'>\displaystyle x </code> & 0 & 1 & 2 & 3 & 4</p><p>Balance (dollars), <code class='latex inline'>\displaystyle y </code> & 100 & 125 & 150 & 175 & 200</p><p>a. Describe this situation in words.</p><p>b. Write the function as a set of ordered pairs.</p><p>c. Plot the ordered pairs in a coordinate plane.</p>

<p>A promoter is holding a video dance. Tickets cost <code class='latex inline'>\$15</code> per person, and he has given away 10 free tickets to radio stations. </p><p>Find how many people bought the ticket if he made <code class='latex inline'>\$600</code>?</p><p>You may use the equation below. </p><p><code class='latex inline'>
\displaystyle
R = 15n - 150
</code></p>

<p>Skylar wants to join the local gym.
The cost in dollars for a membership can be expressed as:
<code class='latex inline'>100 + 39.99m</code></p><p>where 100 is the initiation fee in dollars, 39.99 is the monthly fee in dollars, and m is the number of months for which a person signs up.</p><p>How much will it cost Skylar to join the gym for 14 months?</p>

<p>Think About a Plan The table at the right shows the number of bagels a shop gives you per "baker's dozen." Write an algebraic expression that gives the rule for finding the number of bagels in any number <code class='latex inline'>\displaystyle b </code> of baker's dozens.</p>
<ul>
<li><p>What is the pattern of increase in the number of bagels?</p></li>
<li><p>What operation can you perform on <code class='latex inline'>\displaystyle b </code> to find the number of bagels?</p><img src="/qimages/12401" /></li>
</ul>
<p>Bagels Baker's nom 5 \begin{tabular}{c|c}Baker's Dozens & Number of Bagels \1 & 13 \2 & 26 \3 & 39 \<code class='latex inline'>\displaystyle b </code> &</p>

<p>Determine the function that describe the following function rules. Show your work.</p>
<ul>
<li>The input is 3 less than the output.</li>
</ul>

<p>Determine the function that describe the following function rules. Show your work.</p>
<ul>
<li>The output is 5 less than the input multiplied by 2.</li>
</ul>

<p>Describe and correct the error in the statement about the relation shown in the table. </p><p><code class='latex inline'>\displaystyle
\begin{array}{|l|l|l|l|l|l|}
\hline Input, \boldsymbol{x} & 1 & 2 & 3 & 4 & 5 \\
\hline Output, \boldsymbol{y} & 6 & 7 & 8 & 6 & 9 \\
\hline
\end{array}
</code></p><p>The relation is not a function. One</p><p>output is paired with two inputs.</p>

<p>Mr. Martinez is a sales representative for an agricultural supply company. He receives a salary and monthly commission. He also receives a bonus each time he reaches a sales goal.</p><p>Let e represent earnings, s represent his salary, c represent his commission, and b represent his bonus. Write an algebraic expression to represent his earnings if he receives four equal bonuses.</p>

<p>Martin wants to build an additional closet in a corner of his bedroom. Because the closet will be in a corner, only two new walls need to be built. The total length of the two new walls must be <code class='latex inline'>12</code> m. Martin wants the length of the closet to be twice as long as the width, as shown in the diagram. </p><p>Let function <code class='latex inline'>f(l)</code> be the sum of the tenth and the width. Find the equation for <code class='latex inline'>f(l)</code>. Show your work.</p>

<p>Determine the equations that describe the following function rules. Show your work.</p>
<ul>
<li>Subtract 2 from the input and then multiply by 3 to find the output.</li>
</ul>

<img src="/qimages/43236" />

<img src="/qimages/1554" />
<ul>
<li>Which musician makes the most money at each level
in the table in part b)?</li>
</ul>

<p>Physics Light travels about <code class='latex inline'>\displaystyle 186,000 \mathrm{mi} / \mathrm{s} </code>. The function <code class='latex inline'>\displaystyle d(t)=186,000 t </code> gives the distance <code class='latex inline'>\displaystyle d(t) </code>, in miles, that light travels in <code class='latex inline'>\displaystyle t </code> seconds. How far does light travel in 30 s?</p>

<p>The points represented by the table lie on a line. Find the slope of the line.</p><p><code class='latex inline'>\displaystyle
\begin{array}{|c|c|}
\hline \boldsymbol{x} & \boldsymbol{y} \\
\hline 6 & 9 \\
11 & 15 \\
16 & 21 \\
21 & 27 \\
\hline
\end{array}
</code></p>

<img src="/qimages/43365" /><p>PROBLEM SOLVING The graph shows the percent <code class='latex inline'>\displaystyle p </code> (in decimal form) of battery power remaining in a laptop computer after <code class='latex inline'>\displaystyle t </code> hours of use. A tablet computer initially has <code class='latex inline'>\displaystyle 75 \% </code> of its battery power remaining and loses <code class='latex inline'>\displaystyle 12.5 \% </code> per hour. Which computer's battery will last longer? Explain. (See Example 5.)</p>