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<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="52508ef4-61c9-4d0c-a195-fa1af657c3c8" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--Q1-->
<div class="os-raise-ib-pset-problem" data-content-id="548dcd73-d585-4139-a459-d6bf8980d9fe" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="Up 9" data-solution-options='["Down 3", "Down 8", "Up 9", "Up 8"]'>
<div class="os-raise-ib-pset-problem-content">
<p>For questions 1 - 3, use the graph below.</p>
<p><img alt="This graph shows four functions on an x, y coordinate plane. The \(x\)-axis runs from negative 8 to 9. The \(y\)-axis runs from negative 8 to 8. The first shows the decreasing function h of x = negative 2 times x plus 2. It passes through the points (0, 2) and (1, 0). The second is an increasing function that shows f of x = 2 times x plus 3. It passes through the points (0, 3) and (-1.5, 0). The third is an increasing function that shows j of x = 2 times x minus 6 and passes through the points (0, -6) and (3, 0). The fourth line is an increasing function where g of x = x divided by 2 minus 4 and passes through the points (0, -4) and (2 ,0)." src="https://k12.openstax.org/contents/raise/resources/4645f08e433b9ec202d22feee234504a8c2cca5e" width="400"></p>
<ol class="os-raise-noindent">
<li>Tell the shift from \(j(x)=2x-6\) to \(f(x)=2x+3\).</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Up 9</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Take a moment to think about what you learned in activity 4.11.2. Are you using it the right way?</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is up 9. </p>
</div>
</div>
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="5eae2be9-0274-4a58-9340-3bca315b5440" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="Vertical reflection, down 1" data-solution-options='["Vertical reflection, up 1", "Vertical reflection, down 1", "Vertical stretch, right 1", "Vertical stretch, left 1"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="1">
<li>Tell the transformations from \(f(x)=2x+3\) to \(h(x)=-2x+2\).</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Vertical reflection, down 1</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.11.2–4.11.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is vertical reflection, down 1. </p>
</div>
</div>
<!--Q3-->
<div class="os-raise-ib-pset-problem" data-content-id="0086830d-c6d4-4fca-b4c6-9e78332d2635" data-problem-type="multiselect" data-solution='["Vertical compression of \\(\\frac12\\)", "Down 4"]' data-solution-options='["Vertical stretch of \\(\\frac12\\)", "Vertical compression of \\(\\frac12\\)", "Up 4", "Down 4", "Right 4", "Left 4"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" type="1">
<li>Describe the transformations made from the parent linear function to achieve \(g(x)=\frac12 x -4\).
<strong>Select two</strong> that apply:
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Vertical compression of \(\frac12\); Down 4</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Take a moment to think about what you learned in activities 4.11.2–4.11.4. Are you using it the right way?</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answers are vertical compression of \(\frac12\), down 4. </p>
</div>
</div>
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="d22bcd2b-aa35-487b-8ddf-30111943cf25" data-problem-type="multiselect" data-solution='["\\(y=-\\frac32x+1\\)", "\\(y=-\\frac32x+7\\)"]' data-solution-options='["\\(y=x+4\\)", "\\(y=x-4\\)", "\\(y=-\\frac32x+1\\)", "\\(y=\\frac32x-7\\)", "\\(y=\\frac32x+1\\)", "\\(y=-\\frac32x+7\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4" type="1">
<li><img alt="This graph shows two lines on an x, y coordinate plane. The \(x\)-axis runs from negative 4 to 6. The \(y\)-axis runs from negative 3 to 8. The first line has the equation y = -3 times x divided by 2 plus 1. The second line has the equation y = -3 times x divided by 2 plus 7. The lines do not cross." src="https://k12.openstax.org/contents/raise/resources/f3e3b6cadf256a648642efc7a4bbf57d0ab390b0" width="400">
<p>What are the equations of the two lines shown? <strong>Select two </strong>that apply:</p>
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=-\frac32x+1\) and \(y=-\frac32x+7\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 4.11.1.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answers are \(y=-\frac32x+1\) and \(y=-\frac32x+7\). </p>
</div>
</div>
<!--Q5-->
<div class="os-raise-ib-pset-problem" data-content-id="356feacc-af8e-4824-9fa8-1fa282e2d1f4" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=-3x-4\)" data-solution-options='["\\(f(x)=3x+4\\)", "\\(f(x)=-3x+4\\)", "\\(f(x)=3x-4\\)", "\\(f(x)=-3x-4\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5" type="1">
<li>The linear function \(f(x)=x\) has a vertical stretch of 3, a vertical reflection, and a vertical shift down 4. Which of the following is the new function?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(f(x)=-3x-4\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Take a moment to think about what you learned in activities 4.11.2–4.11.4. Are you using it the right way?</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(f(x)=-3x-4\). </p>
</div>
</div>
<!--Q6-->
<div class="os-raise-ib-pset-problem" data-content-id="90cae9a1-c577-4ffa-a698-0752ff5525af" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=\frac13x+2\)" data-solution-options='["\\(f(x)=\\frac13x+2\\)", "\\(f(x)=-\\frac13x+2\\)", "\\(f(x)=2x+\\frac13\\)", "\\(f(x)=2x-\\frac13\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6" type="1">
<li>The linear function \(f(x)=x\) has a vertical compression of \(\frac13\) and a vertical shift up 2. Which of the following is the new function?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(f(x)=\frac13x+2\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.11.2–4.11.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(f(x)=\frac13x+2\). </p>
</div>
</div>
<!--Q7-->
<div class="os-raise-ib-pset-problem" data-content-id="23cd6648-507a-4211-b236-f0868aca4911" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-\frac34x+7\)" data-solution-options='["\\(y=3x+7\\)", "\\(y=\\frac34x+7\\)", "\\(y=-\\frac34x+7\\)", "\\(y=-\\frac43x+7\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7" type="1">
<li>What is the equation of the function graphed?
<p><img alt="This graph shows a linear function graphed on an x y coordinate plane. The x axis is labeled from negative 2 to 8 and the y axis is labeled from negative 1 to 8. The function f is graph along the points (0, 7) and (4, 4)." class="img-fluid atto_image_button_text-bottom" height="214" src="https://k12.openstax.org/contents/raise/resources/ad267d8ce45e7410c4a1abb402789284ed15ea9c" width="300"></p>
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=-\frac34x+7\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Take a moment to think about what you learned in activities 4.11.1–4.11.4. Are you using it the right way?</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=-\frac34x+7\). </p>
</div>
</div>
<!--Q8-->
<div class="os-raise-ib-pset-problem" data-content-id="a257dca8-2c02-47e2-bc99-3ccbffc3ed08" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=\frac13x -2\)" data-solution-options='["\\(f(x)=\\frac13x -2\\)", "\\(f(x)=-\\frac13x-2\\)", "\\(f(x)=2x+\\frac13\\)", "\\(f(x)=2x - \\frac13\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8" type="1">
<li>The linear function \(f(x)=x\) has a vertical compression of \(\frac13\) and a vertical shift down 2. Which of the following is the new function?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(f(x)=\frac13x -2\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.11.2–4.11.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(f(x)=\frac13x -2\)</p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="67af96c8-1a0c-4c07-9b8b-a709e7d55dbb" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="A translation to the right \(c\) units followed by a reflection across the \(x\)-axis" data-solution-options='["A translation to the right \\(c\\) units followed by a reflection across the \\(x\\)-axis", "A translation to the left \\(c\\) units followed by a reflection across the \\(x\\)-axis", "A translation to the right \\(c\\) units followed by a reflection across the \\(y\\)-axis", "A translation to the left \\(c\\) units followed by a reflection across the \\(y\\)-axis"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9" type="1">
<li>Which two transformations can be used to obtain the graph of \(g(x) = -(x-c)\) from the graph of \(g(x) = x\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! A translation to the right \(c\) units followed by a reflection across the \(x\)-axis.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.11.2 and 4.11.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: A translation to the right \(c\) units followed by a reflection across the \(x\)-axis.</p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="a458c908-a4d6-4aaa-8e32-532cf9418259" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="The graph of \(h\) is the result of the graph of \(g\) being translated left 14 units and down 12 units." data-solution-options='["The graph of \\(h\\) is the result of the graph of \\(g\\) being translated right 14 units and down 12 units.", "The graph of \\(h\\) is the result of the graph of \\(g\\) being translated left 14 units and down 12 units.", "The graph of \\(h\\) is the result of the graph of \\(g\\) being translated right 14 units and up 12 units.", "The graph of \\(h\\) is the result of the graph of \\(g\\) being translated left 14 units and up 12 units."]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="10" type="1">
<li>For the functions \(h\) and \(g\), which statement is true if \(h(x) = g(x + 14) - 12\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph of \(h\) is the result of the graph of \(g\) being translated left 14 units and down 12 units.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 4.11.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The graph of \(h\) is the result of the graph of \(g\) being translated left 14 units and down 12 units.</p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="14fc61a9-cead-4fcb-b070-e24a7df09970" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="Vertical stretch" data-solution-options='["Vertical shrink or compression", "Vertical shift down", "Vertical shift up", "Vertical stretch"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="11" type="1">
<li>Which type of transformation can be used to obtain the graph of \(g(x) = 4(2 + x)\) from the graph of \(f(x) = 2+x\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The correct transformation is a Vertical stretch.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 4.11.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: Vertical stretch.</p>
</div>
</div>
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<div class="os-raise-ib-pset-correct-response">
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</div>
<div class="os-raise-ib-pset-encourage-response">
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</div>
</div>