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Similar Question 1
<p>For each function g(x), identify the value of a or k and describe how the graph of g(x) can be obtained from the graph of f(x).</p><p><code class='latex inline'>g(x) = f(\dfrac{1}{7} x)</code></p>
Similar Question 2
<p>Describe a transformation <code class='latex inline'>p(x)</code> that can be applied to <code class='latex inline'>f(x)</code> that gives the same result as the two transformations applied as</p><p>a) <code class='latex inline'>g(x) = f(x + 6) = 5 </code><br> b) <code class='latex inline'>h(x) = g(x -4) -3</code>.</p><p>Show your work.</p>
Similar Question 3
<p>Sketch a graph and determine an equation for each transformed function. </p><p>i) <code class='latex inline'>g(x) = 4f(-x + 5)</code><br> ii) <code class='latex inline'>h(x) = -f(\frac{1}{4}x - 1) + 3</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><code class='latex inline'>(2, 1)</code> is a point on the graph of <code class='latex inline'>y =f(x)</code>. Find the corresponding point on the graph of each of the following functions.</p><p><code class='latex inline'>\displaystyle y =f(x -2) + 2 </code></p>
<p>Given the graph of the function <code class='latex inline'>f(x)</code>, sketch each graph of <code class='latex inline'>g(x)</code>.</p><img src="/qimages/24522" /><p><code class='latex inline'>g(x) = f(2x) + 5</code></p>
<p>Reflect the given graph on the y-axis.</p><img src="/qimages/5235" />
<p><code class='latex inline'>(2, 1)</code> is a point on the graph of <code class='latex inline'>y =f(x)</code>. Find the corresponding point on the graph of each of the following functions.</p><p><code class='latex inline'>\displaystyle y = -f(-x)+2</code></p>
<p>Compare each transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of <code class='latex inline'>a, k, d,</code> and <code class='latex inline'>c</code>. Then describe, in the appropriate order, the transformations that must be applied to a base function <code class='latex inline'>f(x)</code> to obtain the transformed function.</p><p>a) <code class='latex inline'>\displaystyle g(x) = f(x + 6)+ 2 </code></p><p>b) <code class='latex inline'>\displaystyle g(x) = f(\frac{1}{3}x) + 7 </code></p>
<p>Reflect the given graph on the y-axis.</p><img src="/qimages/5236" />
<p>a) State the base function <code class='latex inline'>f(x)</code> that correspond to each transformed function, <code class='latex inline'>g(x)</code>. </p> <ul> <li>i) <code class='latex inline'>g(x) = \frac{1}{x - 9} + 4</code><br></li> <li>ii) <code class='latex inline'>g(x) = \sqrt{x + 5} - 7</code><br></li> </ul> <p>b) Describe the transformations that are applied to the base function to obtain each function in part a).<br> c) For each function in part a) write the equations for<br> <code class='latex inline'>k(x)</code>: a reflection in the <em>x</em>-axis,<br> <code class='latex inline'>p(x)</code>: a reflection in the <em>y</em>-axis, and<br> <code class='latex inline'>q(x)</code>: a reflection in the <em>x</em>-axis and in the <em>y</em>-axis. </p>
<p>What transformations are applied to <code class='latex inline'>y = f(x)</code> to obtain the graph of <code class='latex inline'>y = af(x-p)+ q</code>, if <code class='latex inline'>a< 0, p<0</code>, and <code class='latex inline'>q< 0</code>?</p><p>a) Vertical stretch by a factor of la|, followed by a translation |p| units to the left and |q| units down</p><p>b) Reflection in the x-axis, vertical stretch by a factor of |a|, followed by a translation |p| units to the right and |a| units down</p><p>c) Reflection in the x-axis, vertical stretch by a factor of |a|, following by a translation |p| units to the left and |q| units down.</p><p>d) Reflection in the x-axis, vertical stretch by a 6 factor of |a|, followed by a translation |p| units to the right and |q| units up</p>
<p>Compare the transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of the parameters a, k, d, and c. Then describe, in the appropriate order, the transformations that must be applied to a base function f(x) to obtain the transformed function.</p><p><code class='latex inline'>g(x) = f(\dfrac{1}{2}x) + 10</code></p>
<p>The point <code class='latex inline'>(3,4)</code> is on the graph of <code class='latex inline'>y=f(x)</code>. State the coordinates of the images on this point on each graph.</p><p><code class='latex inline'> \displaystyle y=f(-4x) </code></p>
<p>Given each graph of a base function <code class='latex inline'>f(x)</code>, sketch the graph of <code class='latex inline'>g(x) = 2f(0.5x - 1.5) + 4</code>.</p><img src="/qimages/24519" />
<p>Given the graph of the function <code class='latex inline'>f(x)</code>, sketch each graph of <code class='latex inline'>g(x)</code>.</p><img src="/qimages/24522" /><p><code class='latex inline'>g(x) = 2f(x + 3)</code></p>
<p>Match each equation with its graph below. Justify your choice. </p><p>a) <code class='latex inline'>y = -\frac{2}{x + 3} + 1</code><br> b) <code class='latex inline'>y = 2\sqrt{-x + 4} - 1</code><br> c) <code class='latex inline'>y = \frac{4}{-x + 2} + 1</code><br> d) <code class='latex inline'>y = \frac{1}{2}\sqrt{x+5} - \frac{5}{2}</code></p><img src="/qimages/24521" />
<p>Each graph represents a transformation of one of the base functions <code class='latex inline'>f(x) = x, f(x) = x^{2}, f(x) = \sqrt{x}</code>, or <code class='latex inline'>f(x) = \frac{1}{x}</code>. State the base function and the equation of the transformed function.</p><img src="/qimages/5232" />
<p>Compare the transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of the parameters a, k, d, and c. Then describe, in the appropriate order, the transformations that must be applied to a base function f(x) to obtain the transformed function.</p><p><code class='latex inline'>g(x) = \dfrac{1}{5} f(x) - 3</code></p>
<p>Given the graph of <code class='latex inline'>f(x)</code>, sketch a graph of each function by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, F&#39;, and G&#39;.</p><img src="/qimages/24170" /><p><code class='latex inline'>n(x) = f(x - 1) + 9</code></p>
<p>Reflect the given graph on the x-axis.</p><img src="/qimages/5234" />
<p>Which of the following equations has a graph in the <code class='latex inline'> x y </code> -plane for which <code class='latex inline'> y </code> is always greater than or equal to <code class='latex inline'> -1 ? </code> </p><p><code class='latex inline'>\displaystyle y=|x|-2 </code></p><p><code class='latex inline'>\displaystyle y=x^{2}-2 </code></p><p><code class='latex inline'>\displaystyle y=(x-2)^{2} </code></p><p><code class='latex inline'>\displaystyle y=x^{3}-2 </code></p>
<p>For each function g(x), identify the value of a or k and describe how the graph of g(x) can be obtained from the graph of f(x).</p><p><code class='latex inline'>g(x) = f(3x)</code></p>
<p>For each function g(x), identify the value of a or k and describe how the graph of g(x) can be obtained from the graph of f(x).</p><p><code class='latex inline'>g(x) = 9f(x)</code></p>
<p>Describe, in the appropriate order, the transformations that must be applied to the base function <code class='latex inline'>f(x)</code> to obtain the transformed function. Then write the corresponding equation and transform the graph of <code class='latex inline'>f(x)</code> to sketch a graph of <code class='latex inline'>g(x)</code>.</p><p><code class='latex inline'>f(x) = \frac{1}{x}</code><br> <code class='latex inline'>g(x) = -3f(x-1)+7</code></p><p>Repeat for <code class='latex inline'>f(x)</code> and the transformed function <code class='latex inline'>g(x)</code></p><p><code class='latex inline'>f(x) = x^2</code><br> <code class='latex inline'>g(x) = -4f[2(x - 1)] + 6</code></p>
<p>Describe the transformation applied to the graph of <code class='latex inline'>f(x)</code> to obtain the graph of <code class='latex inline'>g(x)</code>. Write the equation for <code class='latex inline'>g(x)</code>.</p><img src="/qimages/24528" />
<p>Describe the transformation applied to the graph of <code class='latex inline'>f(x)</code> to obtain the graph of <code class='latex inline'>g(x)</code>. Write the equation for <code class='latex inline'>g(x)</code>.</p><img src="/qimages/24529" />
<p>State the transformed function <code class='latex inline'>g(x) = f(x + 6) + 5</code> for each of the base functions <code class='latex inline'>f(x) = x, g(x) = x^2, f(x) = \sqrt{x}</code>, and <code class='latex inline'>f(x) =\frac{1}{x}</code>. Use words to describe how each base function is transformed.</p>
<p>Reflect the given graph on the x-axis.</p><img src="/qimages/5237" />
<p><code class='latex inline'>(3, 5)</code> is a point on the graph of <code class='latex inline'>y = f(x)</code>. Find the corresponding point on the graph of each of the following relations.</p><p><code class='latex inline'>\displaystyle y = 3(-x + 1) + 2 </code></p>
<p>For each function g(x), identify the value of a or k and describe how the graph of g(x) can be obtained from the graph of f(x).</p><p><code class='latex inline'>g(x) = f(\dfrac{1}{7} x)</code></p>
<p>Given the graph of <code class='latex inline'>f(x)</code>, sketch a graph of each function by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, F&#39;, and G&#39;.</p><img src="/qimages/24170" /><p><code class='latex inline'>h(x) = f(x - 3)</code></p>
<p>Compare each transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of <code class='latex inline'>a, k, d,</code> and <code class='latex inline'>c</code>. Then describe, in the appropriate order, the transformations that must be applied to a base function <code class='latex inline'>f(x)</code> to obtain the transformed function.</p><p>a) <code class='latex inline'>\displaystyle g(x) = 3f(x - 5) </code></p><p>b) <code class='latex inline'>\displaystyle g(x) = \frac{1}{4}f(x) + 4 </code></p>
<p>For each function <code class='latex inline'>f(x)</code> in question 1, sketch a graph of <code class='latex inline'>k(x) = -f(-x).</code> State the domain and range of each function. </p>
<p>Compare each transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of <code class='latex inline'>a, k, d,</code> and <code class='latex inline'>c</code>. Then describe, in the appropriate order, the transformations that must be applied to a base function <code class='latex inline'>f(x)</code> to obtain the transformed function.</p><p><code class='latex inline'>\displaystyle g(x) = 3f(x - 5) </code></p><p>Repeat for each transformed function <code class='latex inline'>g(x)</code></p><p> <code class='latex inline'>\displaystyle g(x) = 4f(3x)-2 </code></p>
<p>Describe a transformation <code class='latex inline'>p(x)</code> that can be applied to <code class='latex inline'>f(x)</code> that gives the same result as the two transformations applied as</p><p>a) <code class='latex inline'>g(x) = f(x + 6) = 5 </code><br> b) <code class='latex inline'>h(x) = g(x -4) -3</code>.</p><p>Show your work.</p>
<p>Reflect the given graph on the y-axis.</p><img src="/qimages/5233" />
<p>Given the graph of <code class='latex inline'>f(x)</code>, sketch a graph of each function by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, F&#39;, and G&#39;.</p><img src="/qimages/24170" /><p><code class='latex inline'>m(x) = f(x + 1)</code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the value of <code class='latex inline'>a</code> or <code class='latex inline'>k</code> and describe how the graph of <code class='latex inline'>g(x)</code> can be obtained from the graph of <code class='latex inline'>f(x)</code>. </p><p>a) <code class='latex inline'>g(x) = 8f(x)</code><br> b) <code class='latex inline'>g(x) = f(6x)</code><br> c) <code class='latex inline'>g(x) = \frac{2}{3}f(x)</code><br> d) <code class='latex inline'>g(x) = f(\frac{1}{9}x)</code> </p>
<p>Given the graph of <code class='latex inline'>f(x)</code>, sketch a graph of each function by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, F&#39;, and G&#39;.</p><img src="/qimages/24170" /><p><code class='latex inline'>r(x) = f(x + 2) - 7</code></p>
<p>Compare each transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of <code class='latex inline'>a, k, d,</code> and <code class='latex inline'>c</code>. Then describe, in the appropriate order, the transformations that must be applied to a base function <code class='latex inline'>f(x)</code> to obtain the transformed function.</p><p><code class='latex inline'>\displaystyle g(x) = f(\frac{1}{3}x) + 7 </code></p><p>Repeat for each transformed function <code class='latex inline'>g(x)</code></p><p> <code class='latex inline'>\displaystyle g(x) = f(-2x) + 6 </code></p>
<p><code class='latex inline'>(2, 1)</code> is a point on the graph of <code class='latex inline'>y =f(x)</code>. Find the corresponding point on the graph of each of the following functions.</p><p><code class='latex inline'>\displaystyle y = 1 -f(1-x) </code></p>
<p>Given the graph of the function <code class='latex inline'>f(x)</code>, sketch each graph of <code class='latex inline'>g(x)</code>.</p><img src="/qimages/24522" /><p><code class='latex inline'>g(x) = f(4x - 16)</code></p>
<p>Given each base function f(x), write the equation of the transformed function g(x). Then transform the graph of f(x) to sketch a graph of g(x).</p><p><code class='latex inline'>f(x) = \dfrac{1}{x}</code></p><p><code class='latex inline'>g(x) = f(x - 4) + 9</code></p>
<p>Reflect the given graph on the x-axis.</p><img src="/qimages/5235" />
<p>Compare the transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of the parameters a, k, d, and c. Then describe, in the appropriate order, the transformations that must be applied to a base function f(x) to obtain the transformed function.</p><p><code class='latex inline'>g(x) = 7f(x -1)</code></p>
<p>For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.</p><p><code class='latex inline'>\displaystyle f(x) = -0.25\sqrt{3(x+ 7)} </code></p>
<p>Compare each transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of <code class='latex inline'>a, k, d,</code> and <code class='latex inline'>c</code>. Then describe, in the appropriate order, the transformations that must be applied to a base function <code class='latex inline'>f(x)</code> to obtain the transformed function.</p><p><code class='latex inline'>\displaystyle g(x) = \frac{1}{4}f(x) + 4 </code></p><p>Repeat for each transformed function <code class='latex inline'>g(x)</code></p><p><code class='latex inline'>\displaystyle g(x) = -5f(x) + 6 </code></p>
<p>Given the graph of the function <code class='latex inline'>f(x)</code>, sketch each graph of <code class='latex inline'>g(x)</code>.</p><img src="/qimages/24522" /><p><code class='latex inline'>g(x) = 3f(-0.5x + 1) - 3</code></p>
<p>Describe the reflection that transforms <code class='latex inline'>f(x)</code> into <code class='latex inline'>g(x)</code>.</p><img src="/qimages/24167" />
<p>For each function g(x), identify the value of a or k and describe how the graph of g(x) can be obtained from the graph of f(x).</p><p><code class='latex inline'>g(x) = \dfrac{2}{5} f(x)</code></p>
<p><code class='latex inline'>(2, 1)</code> is a point on the graph of <code class='latex inline'>y =f(x)</code>. Find the corresponding point on the graph of each of the following functions.</p><p><code class='latex inline'>\displaystyle y = 0.3f(5(x-3)) </code></p>
<p><code class='latex inline'>(2, 1)</code> is a point on the graph of <code class='latex inline'>y =f(x)</code>. Find the corresponding point on the graph of each of the following functions.</p><p><code class='latex inline'>\displaystyle y =f(-2(x+ 9)) - 7 </code></p>
<p>Sketch a graph and determine an equation for each transformed function. </p><p>i) <code class='latex inline'>g(x) = 4f(-x + 5)</code><br> ii) <code class='latex inline'>h(x) = -f(\frac{1}{4}x - 1) + 3</code></p>
<p>Given the graph of <code class='latex inline'>f(x)</code>, sketch a graph of each function by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, F&#39;, and G&#39;.</p><img src="/qimages/24170" /><p><code class='latex inline'>g(x) = f(x) - 4</code></p>
<p>Compare each transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of <code class='latex inline'>a, k, d,</code> and <code class='latex inline'>c</code>. Then describe, in the appropriate order, the transformations that must be applied to a base function <code class='latex inline'>f(x)</code> to obtain the transformed function.</p><p>a) <code class='latex inline'>\displaystyle g(x) = f(2x)-8 </code></p><p>b) <code class='latex inline'>\displaystyle g(x) = 5f(x) - 3 </code></p>
<p>Reflect the given graph on the y-axis.</p><img src="/qimages/5234" />
<p>Compare the transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of the parameters a, k, d, and c. Then describe, in the appropriate order, the transformations that must be applied to a base function f(x) to obtain the transformed function.</p><p><code class='latex inline'>g(x) = f(x + 9) + 8</code></p>
<p><code class='latex inline'>(2, 1)</code> is a point on the graph of <code class='latex inline'>y =f(x)</code>. Find the corresponding point on the graph of each of the following functions.</p><p><code class='latex inline'>\displaystyle y = -f(2(x - 8)) </code></p>
<p>Compare each transformed equation to <code class='latex inline'>y = af[k(x - d)] + c</code> to determine the values of <code class='latex inline'>a, k, d,</code> and <code class='latex inline'>c</code>. Then describe, in the appropriate order, the transformations that must be applied to a base function <code class='latex inline'>f(x)</code> to obtain the transformed function.</p><p> <code class='latex inline'>\displaystyle g(x) = f(x + 6)+ 2 </code></p><p>Repeat for each transformed function <code class='latex inline'>g(x)</code></p><p> <code class='latex inline'>\displaystyle g(x) = \frac{1}{3}f(x - 8) + 1 </code></p>
<p>Reflect the given graph on the y-axis.</p><img src="/qimages/5237" />
<p>Given each base function f(x), write the equation of the transformed function g(x). Then transform the graph of f(x) to sketch a graph of g(x).</p><p><code class='latex inline'>f(x) = \sqrt x</code></p><p><code class='latex inline'>g(x) = 3f(2x)</code></p>
<p>a) Copy and complete the table of values. </p><img src="/qimages/24523" /><p>b) Sketch a graph of the functions on the same set of axes.<br> c) Explain how the points on the graphs of <code class='latex inline'>g(x)</code> and <code class='latex inline'>h(x)</code> relate to the transformation. </p>
<p>Given the graph of <code class='latex inline'>f(x)</code>, sketch a graph of each function by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, F&#39;, and G&#39;.</p><img src="/qimages/24170" /><p><code class='latex inline'>b(x) = f(x) + 6</code></p>
<p>Reflect the given graph on the x-axis.</p><img src="/qimages/5236" />
<p>Match each equation with its graph below. Justify your choice. </p><p>a) <code class='latex inline'>y = \frac{2}{x + 4} - 3</code><br> b) <code class='latex inline'>y = \frac{1}{2}\sqrt{-x + 4} + 3</code><br> c) <code class='latex inline'>y = 3\sqrt{x - 2} + 1</code><br> d) <code class='latex inline'>y = [\frac{1}{4}(x - 5)]^2 + 2</code></p><img src="/qimages/24520" />
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