20. Q20b
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Similar Question 1
<p>The graph of <code class='latex inline'>y=2x^2</code> is narrower than the graph of <code class='latex inline'>y=x^2</code>. How do the following graphs compare?</p><p><code class='latex inline'>y=\frac{2}{x}</code> and <code class='latex inline'>y=\frac{1}{x}</code> </p>
Similar Question 2
<p>Compare each polynomials function with the equation <code class='latex inline'>y = a[k(x -d)]^n + c</code>. State the value of the parameters <code class='latex inline'>a, k, d</code>, and <code class='latex inline'>c</code> and the degree <code class='latex inline'>n</code>, assuming that the base function is a power function. Describe the transformation that corresponds to each parameter.</p><p><code class='latex inline'>y = 0.4(x + 2)^2</code></p>
Similar Question 3
<p>Describe the transformations that must be applied to the graph of each power function, <code class='latex inline'>f(x)</code>, to obtain the transformed function. Write the full equation of the transformed function.</p><p><code class='latex inline'>f(x) = x^3, </code>, <code class='latex inline'> \displaystyle y = 2f[\frac{1}{3}(x - 5)] - 2 </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>The red graph has been compressed horizontally by the factor <code class='latex inline'>\frac{1}{3}</code> relative to the graph of <code class='latex inline'>y=x^2</code>. Write the equation of the red graph.</p><img src="/qimages/2767" />
<p>Describe the transformations in words and note any invariant points.</p><p><code class='latex inline'> \displaystyle y=\frac{1}{(\frac{1}{2}x)}, y=\frac{1}{(\frac{1}{4}x)} </code></p>
<p>Compare each polynomials function with the equation <code class='latex inline'>y = a[k(x -d)]^n + c</code>. State the value of the parameters <code class='latex inline'>a, k, d</code>, and <code class='latex inline'>c</code> and the degree <code class='latex inline'>n</code>, assuming that the base function is a power function. Describe the transformation that corresponds to each parameter.</p><p><code class='latex inline'>y = \frac{3}{5}[-(x -4)]^3 + 1</code></p>
<p> Sketch the graph.</p><p><code class='latex inline'> \displaystyle P(x) = -\frac{1}{2}(x - 2)^5 </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 y=| \frac{1}{3}x |, y = | \frac{1}{5}x| </code></p>
<p>If <code class='latex inline'>f(x) = (x - 2)(x + 5)</code>, determine the x-intercepts for the function <code class='latex inline'>y=-4f(x)</code>.</p>
<p>Describe the transformations in words and note any invariant points.</p><p><code class='latex inline'> \displaystyle y=(2x)^2, y=(5x)^2 </code></p>
<p> Sketch the graph.</p><p><code class='latex inline'> \displaystyle P(x) = 2(x - 1)^5 + 4 </code></p>
<p>For <code class='latex inline'> \displaystyle f(x) =\frac{1}{x} </code></p><p><strong>(a)</strong> Apply a horizontal stretch with factor 2.</p><p><strong>(b)</strong> Apply a vertical stretch with factor 2. What do you notice?</p><p><strong>(c)</strong> What do you notice from the results of a) and b)?</p>
<p>Describe the transformations in words and note any invariant points.</p><p><code class='latex inline'> \displaystyle y=\sqrt{3x}, y= \sqrt{4x} </code></p>
<p>Describe the relationship between the graph of <code class='latex inline'>y = x^2</code> and the graph of <code class='latex inline'>y = 2(x - 3)^2 + 1.</code></p>
<p>Sketch a graph of <code class='latex inline'>y = 4[3(x + 2)]^4 -6</code></p>
<p>Sketch the following.</p> <ul> <li>i. <code class='latex inline'>y = -\frac{1}{4}x^3</code></li> <li>ii. <code class='latex inline'>y = x^3 -1</code></li> <li>iii. <code class='latex inline'>y = (-\frac{1}{4}x)^5</code></li> <li>iv. <code class='latex inline'>y = -x^4</code></li> </ul>
<p>The graph of <code class='latex inline'>y=2x^2</code> is narrower than the graph of <code class='latex inline'>y=x^2</code>. How do the following graphs compare?</p><p><code class='latex inline'>y=2\sqrt{x}</code> and <code class='latex inline'>y=\sqrt{x}</code></p>
<p>The graph of <code class='latex inline'>y=2x^2</code> is narrower than the graph of <code class='latex inline'>y=x^2</code>. How do the following graphs compare?</p><p><code class='latex inline'>y=\frac{2}{x}</code> and <code class='latex inline'>y=\frac{1}{x}</code> </p>
<p>The graph of <code class='latex inline'>y=2x^2</code> is narrower than the graph of <code class='latex inline'>y=x^2</code>. How do the following graphs compare?</p><p><code class='latex inline'>y=2|x|</code> and <code class='latex inline'>y=|x|</code></p>
<p>Compare each polynomials function with the equation <code class='latex inline'>y = a[k(x -d)]^n + c</code>. State the value of the parameters <code class='latex inline'>a, k, d</code>, and <code class='latex inline'>c</code> and the degree <code class='latex inline'>n</code>, assuming that the base function is a power function. Describe the transformation that corresponds to each parameter.</p><p><code class='latex inline'>y = 0.4(x + 2)^2</code></p>
<p>Describe the transformations that must be applied to the graph of each power function, <code class='latex inline'>f(x)</code>, to obtain the transformed function. Write the full equation of the transformed function.</p><p><code class='latex inline'>f(x) = x^3, y = -0.5f(x -4)</code></p>
<p>One of the parent functions <code class='latex inline'>f(x) = x^2, f(x)= \sqrt{x}, f(x) = \frac{1}{x}</code>, and <code class='latex inline'>f(x) =|x|</code> has undergone a transformation of the form <code class='latex inline'>f(kx)</code>. Determine the equations of the transformed functions graphed in red.</p><img src="/qimages/860" />
<p>Describe the transformations that must be applied to the graph of each power function, <code class='latex inline'>f(x)</code>, to obtain the transformed function. Write the full equation of the transformed function.</p><p><code class='latex inline'>f(x) = x^3, </code>, <code class='latex inline'> \displaystyle y = 2f[\frac{1}{3}(x - 5)] - 2 </code></p>
<p>Given a base function <code class='latex inline'>f(x) = x^4</code>, list the parameters of the polynomial function <code class='latex inline'>y = -3[\frac{1}{2}(x+ 4)]^4 + 1</code></p>
<p>Suppose you are asked to graph <code class='latex inline'>y = f(2x + 4)</code>. What two transformations are required? Does the order in which you apply these transformations make a difference? </p>
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