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Similar Question 1
<p>Consider the parent function <code class='latex inline'>y = x^2</code>.</p> <ul> <li>What is the transformation that produced the equation <code class='latex inline'>y = 4x^2</code>?</li> <li>What is the transformation that produced the equation <code class='latex inline'>y=(2x)^2</code>?</li> <li>Why does the two transformations produce the same equation and graph? Show algebraically.</li> </ul>
Similar Question 2
<p>The ordered pairs <code class='latex inline'>(2, 3), (4, 7), (-2, 5)</code>, and <code class='latex inline'>(-4, 6)</code> belong to a function <code class='latex inline'>f</code>. List the ordered pairs that belong to the following:</p><p><code class='latex inline'>y = 2f(x+1)-3 </code></p>
Similar Question 3
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'>y=3f(x) - 1</code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>State the transformations defined by each equation in the order they would be applied to <code class='latex inline'>y= f(x)</code>.</p><p><code class='latex inline'>y = f(2(x-1))</code></p>
<p>State the transformations defined by each equation in the order they would be applied to <code class='latex inline'>y= f(x)</code>.</p><p><code class='latex inline'>y = -f(x- 3)+2</code></p>
<p>State the transformations defined by each equation in the order they would be applied to <code class='latex inline'>y= f(x)</code>.</p><p><code class='latex inline'>y = -2f(4x)</code></p>
<p>Using <code class='latex inline'>f(x) = x^2</code> as the parent function, graph the transformations described by</p> <ul> <li><code class='latex inline'>g(x) = f(3(x + 2))</code></li> <li><code class='latex inline'>h(x) = f(3x + 6)</code></li> </ul> <p>Which of the following statements is true?</p>
<p>The point <code class='latex inline'>(1, 8)</code> is on the graph of <code class='latex inline'>y = f(x)</code>. What are the corresponding coordinates of this point on the following graph?</p><p><code class='latex inline'>y = -f(4(x+1))</code></p>
<p>Given <code class='latex inline'>f(x) =x^3-3x^2, g(x) =f(x-1)</code>, and <code class='latex inline'>h(x)= -f(x)</code>, which of the following correctly describes the transformation of <code class='latex inline'>f</code> for <code class='latex inline'>g</code> and <code class='latex inline'>h</code>?</p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'>y=3f(x) - 1</code></p>
<p>Consider the parent function <code class='latex inline'>y = x^2</code>.</p> <ul> <li>What is the transformation that produced the equation <code class='latex inline'>y = 4x^2</code>?</li> <li>What is the transformation that produced the equation <code class='latex inline'>y=(2x)^2</code>?</li> <li>Why does the two transformations produce the same equation and graph? Show algebraically.</li> </ul>
<p>The point <code class='latex inline'>(1, 8)</code> is on the graph of <code class='latex inline'>y = f(x)</code>. What are the corresponding coordinates of this point on the following graph? <code class='latex inline'>y = -f(-x)</code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'>y=2f( - (x - 3)) + 1</code></p>
<p>What are the transformations that produce <code class='latex inline'>y = f(3(x + 2))</code>?</p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'> y=-3f(2(x - 1)) - 3 </code></p>
<p>The ordered pairs <code class='latex inline'>(2, 3), (4, 7), (-2, 5)</code>, and <code class='latex inline'>(-4, 6)</code> belong to a function <code class='latex inline'>f</code>. List the ordered pairs that belong to the following:</p><p><code class='latex inline'>y = 2f(x+1)-3 </code></p>
<p>State the transformations defined by each equation in the order they would be applied to <code class='latex inline'>y= f(x)</code>.</p><p><code class='latex inline'> y = \frac{1}{2}f(\frac{1}{4}(x - 5)) + 6 </code></p>
<p>For the following equation, what is the parent function and the transformation that are applied? What does the graph of the transformed function look like? Show your work.</p><p><code class='latex inline'> y = \sqrt{2(x -6)} </code></p>
<p>The point <code class='latex inline'>(2, 3)</code> is on the graph of <code class='latex inline'>y = f(x)</code>. What are the corresponding coordinates of this point on the graph of <code class='latex inline'>y = -2f(2(x+5))-4</code>?</p>
<p>State the transformations defined by each equation in the order they would be applied to <code class='latex inline'>y= f(x)</code>.</p><p><code class='latex inline'>y = -f(-(x +2))- 3</code></p>
<p>The point <code class='latex inline'>(3, 6)</code> is on the graph of <code class='latex inline'>y = 2f(x + 1) -4</code>. What is the original point on the graph of <code class='latex inline'>y = f(x)</code>? Show your work.</p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'>y=f(2x) - 5</code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p> <code class='latex inline'> \displaystyle y = 4f(-x) - 4 </code></p>
<p><code class='latex inline'>\displaystyle \begin{array}{|c|c|c|c|} \hline \mathrm{x} & f(x)=\sqrt{x} & r(x)=f(x)+7 & s(x)=f(x-1) \\ \hline 0 & & & \\ \hline 1 & & & \\ \hline 4 & & & \\ \hline 9 & & & \\ \hline \end{array} </code></p><p><strong>(a)</strong> Copy and complete the table of values.</p><p><strong>(b)</strong> Use the points to graph all three functions on the same set of axes.</p><p><strong>(c)</strong> Explain how the points of the translated functions relate to the actual transformations. </p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'>y=f(\frac{1}{3}(x + 4))</code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'> \displaystyle y = f(x - 2) + 3 </code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'> \displaystyle y = \frac{2}{3}f(x + 3) + 1 </code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'> \displaystyle y = -f(\frac{1}{2}x) -2 </code></p>
<p>The point <code class='latex inline'>(1, 8)</code> is on the graph of <code class='latex inline'>y = f(x)</code>. What are the corresponding coordinates of this point on the following graph?</p><p><code class='latex inline'>y = 0.5f(0.5(x + 3))+ 3</code></p>
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