10. Q10d
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Similar Question 1
<ul> <li>Given <code class='latex inline'>f(x) = \frac{1}{x}</code>, write each as a function of <code class='latex inline'>f(x)</code>.<br></li> <li>Then transform the points on <code class='latex inline'>f(x): \{(0, 0), (1, 1), (-1, -1)\}</code> according to the transformation mapping.<br></li> </ul> <p>Show your work by sketching the function.</p><p><code class='latex inline'>\displaystyle y = \frac{1}{2}f(-x) </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 compression by the factor <code class='latex inline'>\frac{1}{2}</code>, a reflection in the y-axis, a translation 3 units left, and a translation 4 units down are applied to <code class='latex inline'>f(x) = \frac{1}{x}</code>.</p>
Similar Question 3
<p>Write an equation of the function which has all of the following transformation from <code class='latex inline'>f(x) = \frac{1}{x}</code>.</p> <ol> <li>Reflections on x-axis</li> <li>Vertical stretch by a factor of 2</li> <li>Horizontal compression of <code class='latex inline'>\frac{1}{4}</code></li> <li>Vertical Shift of 5 units up</li> <li>Horizontal Shift 3 units to left</li> </ol>
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 reciprocal function, </p> <ul> <li>i) write an equation to represent the vertical asymptote </li> <li>ii) write an equation not represent the horizontal asymptote</li> <li>iii) determine the y-intercept</li> </ul> <p><code class='latex inline'>\displaystyle f(x) = \frac{2}{x + 6}</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 compression by the factor <code class='latex inline'>\frac{1}{2}</code>, a reflection in the y-axis, a translation 3 units left, and a translation 4 units down are applied to <code class='latex inline'>f(x) = \frac{1}{x}</code>.</p>
<p>Describe the transformations that you would apply to the graph of <code class='latex inline'>f(x) = \frac{1}{x}</code> to transform it into each of these graphs.</p><p> <code class='latex inline'> \displaystyle y = \frac{1}{2x} </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 = 4 + \frac{4}{5x - 15} </code></p>
<p>Write an equation of the function which has all of the following transformation from <code class='latex inline'>f(x) = \frac{1}{x}</code>.</p> <ol> <li>Reflections on x-axis</li> <li>Vertical stretch by a factor of 2</li> <li>Horizontal compression of <code class='latex inline'>\frac{1}{4}</code></li> <li>Vertical Shift of 5 units up</li> <li>Horizontal Shift 3 units to left</li> </ol>
<p>Describe the transformations that you would apply to the graph of <code class='latex inline'>f(x) = \frac{1}{x}</code> to transform it into each of these graphs.</p><p><code class='latex inline'> \displaystyle y = 0.5(\frac{1}{x}) </code></p>
<ol> <li>State the domain, </li> <li>Range, and </li> <li>equations of the asymptotes and </li> <li>the x and y intercepts</li> </ol> <p><code class='latex inline'>\displaystyle f(x) = \frac{1}{x - \frac{1}{4}}</code></p>
<p>Which of the following is the graph of the function? Describe the intervals where the slope is increasing and the intervals where it is decreasing.</p><p><code class='latex inline'>\displaystyle f(x) = \frac{5}{3 - 2x}</code></p>
<p>Sketch the graph.</p><p><code class='latex inline'>\displaystyle h(x) = \frac{1}{3x - 5}</code></p>
<p> Given <code class='latex inline'>f(x) = \frac{1}{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), (-1, -1)\}</code> according to the transformation mapping. Sketch the function.</p><p><code class='latex inline'>\displaystyle y = 4 + \frac{1}{2x - 2} </code></p>
<p> Given <code class='latex inline'>f(x) = \frac{1}{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), (-1, -1)\}</code> according to the transformation mapping. Sketch the function.</p><p><code class='latex inline'>\displaystyle y = \frac{1}{3x + 9} </code></p>
<ol> <li>State the domain, </li> <li>Range, and </li> <li>equations of the asymptotes and </li> <li>the x and y intercepts</li> </ol> <p><code class='latex inline'>\displaystyle f(x) = -\frac{3}{2x - 5}</code></p>
<ul> <li>Given <code class='latex inline'>f(x) = \frac{1}{x}</code>, write each as a function of <code class='latex inline'>f(x)</code>.<br></li> <li>Then transform the points on <code class='latex inline'>f(x): \{(0, 0), (1, 1), (-1, -1)\}</code> according to the transformation mapping.<br></li> </ul> <p>Show your work by sketching the function.</p><p><code class='latex inline'>\displaystyle y = \frac{1}{2}f(-x) </code></p>
<p>What is the equation of the parent function of <code class='latex inline'>\displaystyle f(x)=\frac{2}{x-2}-4 </code> ? <code class='latex inline'>\displaystyle \begin{array}{ll}\text { a) } g(x)=2^{x} & \text { c) } g(x)=x^{2} \\ \text { b) } g(x)=\frac{2}{x} & \text { d) } g(x)=\frac{1}{x}\end{array} </code></p>
<p>Which of the following is the graph of the function? Describe the intervals where the slope is increasing and the intervals where it is decreasing.</p><p><code class='latex inline'>\displaystyle f(x) = \frac{3}{2x + 7}</code></p>
<p>Sketch the graph.</p><p><code class='latex inline'>\displaystyle g(x) = \frac{1}{2x - 5}</code></p>
<p> Given <code class='latex inline'>f(x) = \frac{1}{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), (-1, -1)\}</code> with transformation mapping.</p><p><code class='latex inline'>\displaystyle y = f(x - 3) + 1 </code></p>
<ol> <li>State the domain, </li> <li>Range, and </li> <li>equations of the asymptotes and </li> <li>the x and y intercepts</li> </ol> <p><code class='latex inline'>\displaystyle f(x) = \frac{1}{2x + 1}</code></p>
<p> Given <code class='latex inline'>f(x) = \frac{1}{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), (-1, -1)\}</code> with transformation mapping.</p><p><code class='latex inline'>\displaystyle y = -3f(\frac{1}{2}x) + 3 </code></p>
<p> Given <code class='latex inline'>f(x) = \frac{1}{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), (-1, -1)\}</code> according to the transformation mapping. Sketch the function.</p><p><code class='latex inline'>\displaystyle y = -\frac{3}{2x} - 3 </code></p>
<ol> <li>State the domain, </li> <li>Range, and </li> <li>equations of the asymptotes and </li> <li>the x and y intercepts</li> </ol> <p><code class='latex inline'>\displaystyle f(x) = \frac{4}{5 - 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) =x</code><br> <code class='latex inline'>g(x) = -4f(x) -6</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) = \frac{1}{x}</code><br> <code class='latex inline'>g(x) = 5f[-(x - 1)] + 2</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) = \frac{1}{x + 3}</code><br> <code class='latex inline'>g(x) = \frac{1}{3 - 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. </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) = \frac{1}{x}</code><br> <code class='latex inline'>g(x) = -3f(x-1)+7</code></p>
<p>Given <code class='latex inline'>f(x) = \frac{1}{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), (-1, -1)\}</code> according to the transformation mapping. State which transformation is applied from the <code class='latex inline'>f(x)</code>.</p> <ol> <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> </ol> <p><code class='latex inline'>\displaystyle y = \frac{1}{x - 3} + 1 </code></p>
<p>Describe the transformations that you would apply to the graph of <code class='latex inline'>f(x) = \frac{1}{x}</code> to transform it into each of these graphs.</p><p><code class='latex inline'> \displaystyle y= \frac{2}{x} </code></p>
<p>Write an equation of the function which has all of the following transformation from <code class='latex inline'>f(x) = \frac{1}{x}</code>.</p> <ol> <li>Reflections on x-axis</li> <li>Reflections on y-axis</li> <li>Vertical stretch by a factor of 3</li> <li>Horizontal compression of <code class='latex inline'>\frac{1}{2}</code></li> <li>No Vertical Shift</li> <li>Horizontal Shift 4 units to right</li> </ol>
<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/23205" />
<p>For <code class='latex inline'>\displaystyle h(x) = \frac{1}{\frac{1}{3}(x -6)} -2 </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 each function f(x), determine the equation for g(x).</p><p><code class='latex inline'>f(x) = \dfrac{1}{x + 7} - 2</code></p><p><code class='latex inline'>g(x) = -f(-x)</code></p>
<p>Analyze the key features (domain, range, vertical asymptotes, and horizontal asymptotes) of each function, and then sketch the function.</p><p><code class='latex inline'>\displaystyle f(x) = \frac{3}{x - 2} + 4</code></p>
<p> Given <code class='latex inline'>f(x) = \frac{1}{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), (-1, -1)\}</code> with transformation mapping.</p><p><code class='latex inline'>\displaystyle y = \frac{1}{2}f(-x) + 1 </code></p>
<ul> <li>Given <code class='latex inline'>f(x) = \frac{1}{x}</code>, write each as a function of <code class='latex inline'>f(x)</code>.<br></li> <li>Then transform the points on <code class='latex inline'>f(x): \{(0, 0), (1, 1), (-1, -1)\}</code> according to the transformation mapping.<br></li> </ul> <p>Show your work by sketching the function.</p><p><code class='latex inline'>\displaystyle y = -3f(-\frac{1}{2}x) </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'>r(x) = \frac{3}{4-x} + 6</code></p>
<p>For each reciprocal function, </p> <ul> <li>i) write an equation to represent the vertical asymptote </li> <li>ii) write an equation not represent the horizontal asymptote</li> <li>iii) determine the y-intercept</li> </ul> <p><code class='latex inline'>\displaystyle f(x) = \frac{5}{1 - x}</code></p>
<p>Determine if g(x) is a reflection of f(x). Justify your answer.</p><p><code class='latex inline'>f(x) = \dfrac{1}{x + 15} - 8</code></p><p><code class='latex inline'>f(x) = -\dfrac{1}{x + 15} + 8</code></p>
<p>Which of the following is the graph of the function? Describe the intervals where the slope is increasing and the intervals where it is decreasing.</p><p><code class='latex inline'>\displaystyle f(x) = -\frac{2}{x + 4}</code></p>
<ol> <li>State the domain, </li> <li>Range, and </li> <li>equations of the asymptotes and </li> <li>the x and y intercepts</li> </ol> <p><code class='latex inline'>\displaystyle f(x) = -\frac{1}{x + 4}</code></p>
<p>Describe the transformations that you would apply to the graph of <code class='latex inline'>f(x) = \frac{1}{x}</code> to transform it into each of these graphs.</p><p> <code class='latex inline'> \displaystyle y = -\frac{1}{x} </code></p>
<ol> <li>State the domain, </li> <li>Range, and </li> <li>equations of the asymptotes and </li> <li>the x and y intercepts</li> </ol> <p><code class='latex inline'>\displaystyle f(x) = -\frac{3}{x + \frac{1}{2}}</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)=\frac{1}{x}</code>, <code class='latex inline'>g(x)=-\frac{1}{x}</code></p>
<p>Given <code class='latex inline'>f(x) = \frac{1}{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), (-1, -1)\}</code> according to the transformation mapping. </p><p><code class='latex inline'>\displaystyle y = 4 + \frac{4}{5x - 15} </code></p>
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