10. Q10
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Similar Question 1
<p> State the transformations that are applied to each parent function, resulting in the given transformed function. Sketch the graphs of the</p><p><code class='latex inline'>g(x) =\sqrt{x}, y= -2g(2x)</code></p>
Similar Question 2
<p>The function <code class='latex inline'>y=f(x)</code> has been transformed to <code class='latex inline'>y=af[k(x - d)] + c</code>. Determine <code class='latex inline'>a, k, c,</code> and <code class='latex inline'>d</code>; sketch the graph and state the domain and range for each transformation.</p><p>A vertical stretch by the factor 2, a reflection in the x-axis, and a translation 4 units right are applied to <code class='latex inline'>y=\sqrt{x}</code>.</p>
Similar Question 3
<p> Graph each function, not by plotting points, but by starting with the graph of parent function <code class='latex inline'>f(x) = |x|</code> given in the lecture and then applying the appropriate transformations.</p><p><code class='latex inline'>\displaystyle y = | 2\sqrt{|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>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <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>, and describe the transformation in the form <code class='latex inline'>y = f(x - d) + c</code> and in words. Then sketch a graph of <code class='latex inline'>g(x)</code> and state the domain and range of each function. </p><p><code class='latex inline'>g(x) = \sqrt{x + 3}</code></p>
<p>Describe the transformation that&#39;s indicated by the arrows.</p><img src="/qimages/864" />
<p>Find the value of <code class='latex inline'>k</code> if the equation of </p><p><code class='latex inline'>y = \sqrt{x + 3} + k </code> passes through the point <code class='latex inline'>(4, -3)</code>.</p>
<p>For each graph, describe the reflection that transforms <code class='latex inline'>f(x)</code> into <code class='latex inline'>g(x)</code>. </p><img src="/qimages/381" />
<p>Which point on the number line is closest to <code class='latex inline'>-\sqrt{7}</code>?</p><img src="/qimages/24322" /><p>A. R</p><p>B. S</p><p>C. T</p><p>D. U</p>
<p>Given <code class='latex inline'>f(x) = \sqrt{x}</code>, sketch each of the following.</p><p><code class='latex inline'> y = \frac{1}{2}f(-x) </code></p>
<p>Each of the following has been transformed from <code class='latex inline'>f(x) = \sqrt{x}</code>. State which of the following transformation it has </p> <ul> <li>Reflections on x-axis</li> <li>Reflections on y-axis</li> <li>Vertical stretch</li> <li>Horizontal compression</li> <li>Vertical Shift</li> <li>Horizontal Shift</li> </ul> <p><code class='latex inline'>\displaystyle y = \sqrt{-3x} </code></p>
<p>Sketch graphs of the pair of transformed functions, along with the graph of the parent function, on the same set of axes. Describe the transformations in words and note any invariant points.</p><p><code class='latex inline'> \displaystyle f(x)=\sqrt{-\frac{1}{2}x}, g(x)=\sqrt{-\frac{1}{3}x} </code></p>
<p>a) Sketch a graph of <code class='latex inline'>f(x) = \sqrt{x}</code> reflected in each given line. Write the equation of the transformed function, <code class='latex inline'>g(x)</code>. </p> <ul> <li>i) <code class='latex inline'>x = -1</code><br></li> <li>ii) <code class='latex inline'>x = -2</code><br></li> <li>iii) <code class='latex inline'>x = -3</code><br></li> </ul> <p>b) In each case, describe two transformations that give the same result as <code class='latex inline'>g(x)</code>.<br> c) Will the results from part b) be true when <code class='latex inline'>f(x) = \sqrt{x}</code> is reflected in the line <code class='latex inline'>x = a</code>, {<code class='latex inline'>a \in \mathbb{R}</code>}? Explain. Write the corresponding transformed function.</p>
<p><code class='latex inline'>f(x)=\sqrt{x+2}+3</code></p><p><strong>(b)</strong> Write the equations for <code class='latex inline'>-f(x)</code>, <code class='latex inline'>f(-x)</code>, and <code class='latex inline'>-f(-x)</code>. Describe the transformation(s) represented by each equation.</p><p><strong>(c)</strong> Sketch the graphs of all four functions on the same set of axes.</p>
<p>If <code class='latex inline'>f(x) = \sqrt{x}</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'> y= -2f(-(x - 2)) + 1</code></p>
<p>Sketch graphs of the pair of transformed functions, along with the graph of the parent function, on the same set of axes. </p><p><code class='latex inline'> \displaystyle f(x)=\sqrt{-3x}, g(x)=\sqrt{-4x} </code></p>
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code> in each case. Verify your answer by graphing. </p><p><code class='latex inline'>f(x)=\sqrt{x-10}+3</code>, <code class='latex inline'>g(x)=-\sqrt{x-10}+3</code></p>
<p>Determine if g(x) is a reflection of f(x). Justify your answer.</p><p><code class='latex inline'>f(x) = \sqrt {x + 7}</code></p><p><code class='latex inline'>g(x) = \sqrt {x - 7}</code></p>
<p>a) Given <code class='latex inline'>f(x) = \sqrt{16 -x^{2}}</code>, write the equations of <code class='latex inline'>f(-x), -f(x),</code> and <code class='latex inline'>-f(-x)</code>. Which functions are equivalent?<br> b) Graph each function. Determine any invariant points.<br> c) State the domain and range of each function. </p>
<p>Determine the domain and range for each of the following and state whether it is a function:</p><p><code class='latex inline'>\displaystyle y = \sqrt{5 -x} </code></p>
<p>The graph of <code class='latex inline'>g(x) = \sqrt{x}</code> is reflected across the <code class='latex inline'>y</code>-axis, stretched vertically by the factor 3, and then translated 5 units right and 2 units down. Draw the graph of the new function and write its equation.</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) = \sqrt{x}</code><br> <code class='latex inline'>g(x) = 2f(4x)</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</code><br> <code class='latex inline'>g(x) = -\frac{1}{3}f[3(x + 2)] - 4</code></p>
<p>For what value of <code class='latex inline'>a</code> is <code class='latex inline'>-\sqrt{a}<-\frac{1}{\sqrt{a}}</code> true?</p><p>A. <code class='latex inline'>\frac{1}{3}</code></p><p>B. -4</p><p>C. 2</p><p>D. 1</p>
<p>The following has been transformed from <code class='latex inline'>f(x) = \sqrt{x}</code>. State which of the following transformation it has </p> <ul> <li>Reflections on x-axis</li> <li>Reflections on y-axis</li> <li>Vertical stretch</li> <li>Horizontal compression</li> <li>Vertical Shift</li> <li>Horizontal Shift</li> </ul> <p><code class='latex inline'>\displaystyle y = -2\sqrt{x} </code></p>
<p> Graph each function, not by plotting points, but by starting with the graph of parent function <code class='latex inline'>f(x) = |x|</code> given in the lecture and then applying the appropriate transformations.</p><p><code class='latex inline'>\displaystyle y = | 2\sqrt{|x|} - 1| </code></p>
<p>Given <code class='latex inline'>f(x) = \frac{1}{x}</code>, write each in terms of <code class='latex inline'>f(x)</code>. </p><p><code class='latex inline'>\displaystyle y = \frac{1}{x + 2} </code></p>
<p>If <code class='latex inline'>f(x) = \sqrt{x}</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'>y=f(-\frac{1}{2}(x + 4)) - 3 </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. </p><p>Then, write the corresponding equation and transform the graph of f(x] to sketch the graph of g(x).</p><p><code class='latex inline'>f(x) = \sqrt{x}</code><br> <code class='latex inline'>g(x) = 2f(4x)</code></p>
<p>The graph of <code class='latex inline'>y = f(x)</code> is given. Match each equation with its graph and give reasons for your choices.</p><p><code class='latex inline'> \begin{array}{cccc} &(a) &y = f(x - 4) &(b)& y = f(x) + 3 \\ &(c) &y = \frac{1}{3}f(x) &(d) &y = -f(x + 4) \\ &(e)& y = 2f(x + 6) \\ \end{array} </code></p><img src="/qimages/242" />
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>.</p><p><code class='latex inline'>f(x) = -\sqrt{x + 4} + 19</code><br> <code class='latex inline'>g(x) = f(-x)</code></p>
<p>Given <code class='latex inline'>f(x) = \sqrt{x}</code>, sketch each of the following.</p><p><code class='latex inline'>y = 2f(x)</code></p>
<p>The diagram at the right shows the distance between a new building and its nearest neighbor. The diagram has a scale of 1 in.: <code class='latex inline'>\displaystyle 100 \mathrm{ft} </code>. What is the actual distance between the buildings, in feet?</p>
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>.</p><p><code class='latex inline'>f(x) = \sqrt{x - 21} + 9</code><br> <code class='latex inline'>g(x) = -f(x)</code></p>
<p>Write a quadratic equation with the given solutions.</p><p><code class='latex inline'>\displaystyle \frac{3+\sqrt{5}}{2}, \frac{3-\sqrt{5}}{2} </code></p>
<p>For each function below,</p><p>i) determine <code class='latex inline'>\displaystyle f(-2), f(1) </code>, and <code class='latex inline'>\displaystyle f\left(\frac{1}{2}\right) </code> ii) write the function in mapping</p><p>notation</p><p>f) <code class='latex inline'>\displaystyle f(x)=\sqrt{3-2 x} </code></p>
<p>The graph of the equation <code class='latex inline'>y=(x-1)^2+2</code> is the graph of a parabola that opens up and has its vertex at (1,2). What do you know about the graphs of the following equations?</p><p><code class='latex inline'> \displaystyle y=\sqrt{x-1} + 2 </code></p>
<p>Find the point of intersection between the root function and the line.</p><p><code class='latex inline'> \begin{array}{cccc} &y = \sqrt{x} + 1 & &y = 3x - 1 \\ \end{array} </code></p>
<p>The graph of <code class='latex inline'>\displaystyle x=y^{2} </code> is shown at the right.</p><p>a. Is this the graph of a function?</p><p>b. How does <code class='latex inline'>\displaystyle x=y^{2} </code> relate to the square root function <code class='latex inline'>\displaystyle y=\sqrt{x} </code> ?</p><p>c. Reasoning What is a function for the part of the graph that is shown in Quadrant IV? Explain.</p><img src="/qimages/60763" />
<p> Sketch the graphs below to show the difference between the two.</p><p><code class='latex inline'> \begin{array}{cccc} &y = \sqrt{|x|} &&y = | \sqrt{x + 1} |\\ \end{array} </code></p>
<p><code class='latex inline'>f(x)=\sqrt{x+2}+3</code></p><p>(b) Write the equations for <code class='latex inline'>-f(x)</code>, <code class='latex inline'>f(-x)</code>, and <code class='latex inline'>-f(-x)</code>. Describe the transformation(s) represented by each equation.</p><p>(c) Sketch the graphs of all four functions on the same set of axes.</p><p>(d) State the domain and range of each function. Describe any similarities or differences. </p><p>(e) Are any points invariant? Explain. Refer the parts (a), (b), (c), (d)</p>
<p>Copy each graph of <code class='latex inline'>f(x)</code> and sketch its reflection in the <code class='latex inline'>x</code>-axis, <code class='latex inline'>g(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/806" />
<p>For <code class='latex inline'>\displaystyle h(x) = 5 - 2\sqrt{3x + 6} </code></p><p>find </p><p>i. the domain and range.</p><p>ii. the relationship to the parent function. including all applied transformations</p><p>iii. a sketch of the function</p>
<p>For the set of functions, transform the graph of <code class='latex inline'>f(x)</code> to sketch <code class='latex inline'>g(x)</code> and <code class='latex inline'>h(x)</code>.</p><p><code class='latex inline'>f(x) = \sqrt{x}, g(x) = \sqrt{\frac{1}{5}x}, h(x) = \sqrt{-5x}</code></p>
<p>For each function g(x), describe the transformation from a base function of <code class='latex inline'>f(x) = x</code>, <code class='latex inline'>f(x) = x^2</code>, <code class='latex inline'>f(x) = \sqrt x</code>, or <code class='latex inline'>f(x) = \dfrac{1}{x}</code>. Then transform the graph of f(x) to sketch a graph of g(x).</p><p><code class='latex inline'>g(x) = \sqrt {\dfrac{x}{3}}</code></p>
<p><code class='latex inline'>f(x)=\sqrt{x+2}+3</code></p><p><strong>(b)</strong> Write the equations for <code class='latex inline'>-f(x)</code>, <code class='latex inline'>f(-x)</code>, and <code class='latex inline'>-f(-x)</code>. Describe the transformation(s) represented by each equation.</p><p><strong>(c)</strong> Sketch the graphs of all four functions on the same set of axes.</p><p><strong>(d)</strong> State the domain and range of each function. Describe any similarities or differences. Refer the parts (a), (b), (c)</p>
<p>Match each function with its graph.</p><img src="/qimages/60730" /><p><code class='latex inline'>\displaystyle y=\sqrt{x}-2 </code></p>
<p>For each function, identify the base function as one of <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>. Sketch the graphs of the base function and the transformed function, and state the domain and range of the functions. </p><p><code class='latex inline'>p(x) = 4\sqrt{x-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/24168" />
<p>Use the base function <code class='latex inline'>f(x)=\sqrt{x}</code>. Write the equation for each transformed function.</p><p><strong>(a)</strong> <code class='latex inline'>n(x)=f(x-4)-6</code></p><p><strong>(b)</strong> <code class='latex inline'>r(x)=f(x+2)+9</code></p><p><strong>(c)</strong> <code class='latex inline'>s(x)=f(x+6)-7</code></p><p><strong>(d)</strong> <code class='latex inline'>t(x)=f(x-11)+4</code></p>
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>f(x)=\sqrt{x+4}-4</code>, <code class='latex inline'>g(x)=-f(x)</code></p>
<p>For the graph of <code class='latex inline'>f(x) = \sqrt{x}</code>, identify the transformation that would not be applied to <code class='latex inline'>f(x)</code> to obtain the graph of <code class='latex inline'>y = 2f(-2x) + 3</code>.</p>
<p>The function <code class='latex inline'>y=f(x)</code> has been transformed to <code class='latex inline'>y=af[k(x - d)] + c</code>. Determine <code class='latex inline'>a, k, c,</code> and <code class='latex inline'>d</code>; sketch the graph and state the domain and range for each transformation.</p><p>A vertical stretch by the factor 2, a reflection in the x-axis, and a translation 4 units right are applied to <code class='latex inline'>y=\sqrt{x}</code>.</p>
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code>. Check by graphing. </p><p><code class='latex inline'>f(x) = \sqrt{x}</code><br> <code class='latex inline'>g(x) = -\sqrt{x}</code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p> <code class='latex inline'>g(x)=\sqrt{x-9}-5</code></p>
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>f(x)=\sqrt{x+9}-1</code>, <code class='latex inline'>g(x)=-f(-x)</code></p>
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code> in each case. Verify your answer by graphing.</p><p><code class='latex inline'>f(x)=\sqrt{x}</code>, <code class='latex inline'>g(x)=\sqrt{-x}</code></p>
<p>Each graph represents a transformation of one of the base functions <code class='latex inline'>f(x) = x</code>, <code class='latex inline'>f(x) = x^2</code>, <code class='latex inline'>f(x) = \sqrt x</code>, or <code class='latex inline'>f(x) = \dfrac{1}{x}</code>. State the base function and the equation of the transformed function.</p><img src="/qimages/23206" />
<img src="/qimages/864" /><p><code class='latex inline'>\displaystyle f(x)=5 \sqrt{-3(x-2)}+4 \leftarrow \mathrm{E} </code></p><p>Match the words with letters.</p><p><code class='latex inline'> \displaystyle \begin{array}{cccccc} &\text{Divide the x-coordinates by 3.} && A\\ &\text{Multiply the y-coordinates by 5.} && B\\ &\text{Multiply the x-coordinates by -1.} && C\\ &\text{Add 4 to the y-coordinates.} && D\\ &\text{Add 2 to the x-coordinates.} && E\\ \end{array} </code></p>
<p>Determine the domain and the range of each function.</p><p><code class='latex inline'>\displaystyle y=\sqrt{4-3 x} </code></p>
<p>Given each graph of <code class='latex inline'>f(x)</code>, graph and label <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>g(x) = f(\frac{x}{4})</code></p><img src="/qimages/24527" />
<p>Determine if g(x) is a reflection of f(x). Justify your answer.</p><p><code class='latex inline'>f(x) = \sqrt {x - 13} + 6</code></p><p><code class='latex inline'>g(x) = -\sqrt {13 - x} - 6</code></p>
<p>Graph the function <code class='latex inline'>y = \sqrt{16 - x^2}</code></p>
<p>Use words and function notation to describe the transformation that can be applied to the graph of <code class='latex inline'>f(x)</code> to obtain the graph of <code class='latex inline'>g(x)</code>. State the domain and range of each function. </p><img src="/qimages/801" />
<p>Error Analysis A student graphed the function <code class='latex inline'>\displaystyle y=\sqrt{x-2} </code> at the right. What mistake did the student make? Draw the correct graph.</p><img src="/qimages/60749" />
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <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>, and describe the transformation in the form <code class='latex inline'>y = f(x - d) + c</code> and in words. Then sketch a graph of <code class='latex inline'>g(x)</code> and state the domain and range of each function. </p><p><code class='latex inline'>g(x) = \sqrt{x} + 9</code></p>
<p>Graph each number on a number line.</p><p><code class='latex inline'>\displaystyle \sqrt{10} </code></p>
<p>Write each function in mapping notation.</p><p>c) <code class='latex inline'>\displaystyle h(b)=\sqrt{9 b+9} </code></p>
<p>For each function <code class='latex inline'>g(x)</code>, describe the transformation from a base function of <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>. Then skctch a graph of <code class='latex inline'>f(x)</code> and <code class='latex inline'>g(x)</code> on the same axes.</p><p><code class='latex inline'>g(x) = \sqrt{\frac{x}{6}}</code></p>
<p>For the function, identify the parent function and describe how the graph of the function can be obtained from the graph of the parent function. </p><p><code class='latex inline'> \displaystyle y=\sqrt{-2x} </code></p>
<p>For each function f(x), determine the equation for g(x).</p><p><code class='latex inline'>f(x) = \sqrt {x - 1} + 8</code></p><p><code class='latex inline'>g(x) = -f(x)</code></p>
<p>Sketch each set of functions on the same set of axes.</p><p><code class='latex inline'>y = \sqrt{x}, y = \sqrt{3x}, y = \sqrt{-3x}, y = \sqrt{-3(x + 1)} - 4</code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>g(x)=\sqrt{x+10}</code></p>
<p>Graph each number on a number line.</p><p><code class='latex inline'>\displaystyle -\sqrt{24} </code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>g(x)=\sqrt{x}-12</code></p>
<p>The blue graph has been stretched horizontally by the factor 2 relative to the graph of <code class='latex inline'>y=\sqrt{x}</code> and then reflected in the y-axis. Write the equation of the blue graph.</p><img src="/qimages/858" />
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code>. Check by graphing. </p><p><code class='latex inline'>f(x) = \sqrt{x + 12} - 7</code><br> <code class='latex inline'>g(x) = -\sqrt{x + 12} - 7</code></p>
<p> Given <code class='latex inline'>f(x) = \sqrt{x}</code>, write each as a function of <code class='latex inline'>f(x)</code>. Then transform the points on <code class='latex inline'>f(x): \{(0, 0), (1, 1), (4, 2)\}</code> according to the transformation mapping.</p><p><code class='latex inline'>\displaystyle y = \frac{\sqrt{3x}}{3} </code></p>
<p>For <code class='latex inline'>f(x) = \sqrt{x}</code>, sketch the graph of <code class='latex inline'>h(x) = f(-3x - 12)</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) =x^2</code><br> <code class='latex inline'>g(x) = f[\frac{1}{2}(x+1)]</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) = \sqrt{x}</code><br> <code class='latex inline'>g(x) = \frac{1}{3}f[2(x + 5)] + 4</code></p>
<p> State the transformations that are applied to each parent function, resulting in the given transformed function. Sketch the graphs of the</p><p><code class='latex inline'>g(x) =\sqrt{x}, y= -2g(2x)</code></p>
<p>Sketch graphs of the pair of transformed functions, along with the graph of the parent function, on the same set of axes. </p><p><code class='latex inline'> \displaystyle f(x)=\sqrt{\frac{1}{2}x}, g(x)=\sqrt{\frac{1}{3}x} </code></p>
<p>Sketch the graph of its reflection in the <code class='latex inline'>y-</code>axis, <code class='latex inline'>h(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/806" />
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