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<h4>Activity</h4>
<p>In an earlier activity, you saw a function representing the area of a square (function \(A\)) and another representing the revenue of a tennis camp (function \(R\)). Refer to the descriptions of those functions to answer these questions.</p>
<ol class="os-raise-noindent">
<li> Here is a graph that represents function \(A\), defined by \(A(s)=s^2\), where \(s\) is the side length of the square in centimeters. </li>
</ol>
<p><img alt="A graph. " src="https://k12.openstax.org/contents/raise/resources/76576c471fa89bdb2f5e278ace7605136df739d5"></p>
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="cd351a2e-c74c-4c6f-8e4a-16b627e2d1f3" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" type="a">
<li>Name three possible input-output pairs of this function. Enter your answers as sets of ordered pairs.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answers:</p>
<p>\(A(2)=4\), \(A(3)=9\), and \(A(7)=49\), or \((2,4)\), \((3,9)\), \((7,49)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="290fceb9-31c0-4471-b95f-72e364d548f1" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2" type="a">
<li>Earlier, we described the set of all possible input values of \(A\) as “any number greater than or equal to 0.” How would you describe the set of all possible output values of \(A\)? </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answers:</p>
<p>The outputs of \(A\) are also all numbers greater than or equal to 0.</p>
</div>
</div>
<br>
<br>
<ol class="os-raise-noindent" start="2">
<li> Function \(R\) is defined by \(R(n)=40n\), where \(n\) is the number of campers.</li>
</ol>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="934a9343-75b3-4508-8a99-25eccc45ec2d" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" type="a">
<li>Is 20 a possible output value in this situation? What about 100? Be prepared to show your reasoning. </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answers:</p>
<p>No, both 20 and 100 cannot be outputs because the input (the number of campers) cannot be fractions. </p>
</div>
</div>
<br>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="8fb3b180-b081-4e76-8875-a619c86c79fb" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2" type="a">
<li>Here are two graphs that relate number of students and camp revenue in dollars. Which graph could represent function \(R\)? Explain why the other one could not represent the function.<br>
<br>
<img alt="A graph. " src="https://k12.openstax.org/contents/raise/resources/4ef73b4c27d99682a72671f9517d57581e0d3589"><br>
<img alt="A graph. " src="https://k12.openstax.org/contents/raise/resources/8e212f8010016b9ef2ed559709268813ad1477b2">
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answers:</p>
<p>The second graph could represent function \(R\). The first graph could not represent function \(R\) because it includes all points for \(n\)-values between 0 and 5, \(n\)-values greater than 16, and fractional \(n\)-values. All of these \(n\)-values don’t apply in this situation.</p>
</div>
</div>
<br>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="ee86ebe5-2b45-4b0f-86c0-5bbc6953f5a6" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3" type="a">
<li>Describe the set of all possible output values of \(R\).</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answers:</p>
<p>The outputs of \(R\) are all multiples of 40 between 200 and 640 (200, 240, 280, and so on). </p>
</div>
</div>
<br>
<p>Write the following definition in your math notebook:
The set of output values form the <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">range</span> of the function.</p>
<h4>Video: Identifying Outputs of a Function</h4>
<p>Watch the following video to learn more about identifying outputs of a function.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><video controls="true" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/21adf0146df228d483924077672ad2140a3bb95d">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/e0decf3ffc5d4cbc1b14b2110a48743a7ffa6739" srclang="en_us">
https://k12.openstax.org/contents/raise/resources/21adf0146df228d483924077672ad2140a3bb95d
</video></div>
</div>
<br>
<br>
<!-- "Start "Are you Ready for More? click to reveal. If you have more than one on a page, you will need to change the Data-fire/data-wait-for-events for each set.-->
<div class="os-raise-ib-cta" data-button-text="Are you ready for more?" data-fire-event="RFM1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-cta-prompt">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="be75f95d-255c-4cec-8a35-4b310ff5afb9" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Making a Real-World Connection </h4>
<p>If the camp wishes to collect at least $500 from the participants, how many students can they have? Explain how this information is shown on the graph.</p>
</div>
<div class="os-raise-ib-input-prompt">
<p>Write your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answers:</p>
<p>They will need at least 13 students to collect $500 or more, so the possibilities are 13, 14, 15, and 16. On the graph, there are only 4 dots that lie on or above the horizontal line representing $500.</p>
</div>
</div>
<!--End interaction-->