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969a5431-73d3-4117-b165-8114bdf3fbdc.html
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<h4>Cool Down Activity </h4>
<p>For questions 1 - 4, match each equation of the linear functions with one of the lines in the given graph.</p>
<p>Match each equation of the linear functions with one of the lines in the given graph.</p>
<p><img alt="Graph of four functions where the orange line has a \(y\)-intercepts at 3 and slope of 2, the baby blue line has a \(y\)-intercepts at 3 and slope of 1/2, the blue line has a \(y\)-intercepts at 3 and slope of -2, and the green line has a \(y\)-intercepts at -3 and slope of 2." src="https://k12.openstax.org/contents/raise/resources/f7b53aade291d174c12865880e32db6f0bf8bb5d"></p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b93f54a2-0f7a-418a-9d14-c65a3a579413" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>\(f(x)=2x+3\)</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 answer:</p>
<p>I</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="caa983eb-37df-446f-842f-2892cc849293" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>\(g(x)=2x−3\)</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 answer:</p>
<p>III</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="e6649b0b-81e1-40b7-bcd4-95bc841c40f1" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>\(h(x)=−2x+3\)</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 answer:</p>
<p>IV</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="38965517-667a-49e9-943a-45954f83fa11" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>\(j(x)=\frac{1}{2}x+3\)</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 answer:</p>
<p>II</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="994deb25-39f3-4a0b-aab6-1e0b86520581" data-retry-limit="2" data-schema-version="1.0">
<div class="os-raise-ib-pset-problem" data-content-id="5f4f2259-2fef-4583-987d-86e9687e8b43" data-problem-type="dropdown" data-retry-limit="2" data-solution="The graph will be shifted 3 units to the right." data-solution-options='["The graph will be shifted 3 units down.", "The graph will be shifted 3 units up.", "The graph will be stretched vertically by a factor of 3.", "The graph will be compressed vertically by a factor of 3.", "The graph will be shifted 3 units to the right.", "The graph will be shifted 3 units to the left.", "The graph will be stretched horizontally by a factor of 3.", "The graph will be compressed horizontally by a factor of 3."]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="5">
<li>How will the graph of k(x) = x be affected if the transformation k(x - 3) is applied?</li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph will be shifted 3 units to the right. This happens because the transformation \(k(x-3)\) moves the graph horizontally to the right by 3 units.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Think about how subtracting from the variable inside the function affects the graph’s position on the horizontal axis.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The graph will be shifted 3 units to the right. By applying the transformation \(k(x - 3)\), the graph is moved 3 units to the right, which shifts each point on the graph horizontally.</p>
</div>
</div>
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<div class="os-raise-ib-pset-correct-response"> </div>
<div class="os-raise-ib-pset-encourage-response"> </div>
</div>