11. Q11i
Save videos to My Cheatsheet for later, for easy studying.
Video Solution
Q1
Q2
Q3
L1
L2
L3
Similar Question 1
<p>The function <code class='latex inline'>y = x^3</code> has undergone each of the following sets of transformations. List three points on the resulting function</p><p>reflected in the x-axis, horizontally compressed by a factor of <code class='latex inline'>\frac{7}{10}</code> , horizontally translated 12 units to the right, vertically translated 6 units up</p>
Similar Question 2
<ul> <li>i) 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. Then, write the corresponding equation.</li> <li>ii) State the domain and range of the transformed function. For even functions, state the vertex and the equation of the axis of symmetry.</li> </ul> <p><code class='latex inline'>\displaystyle f(x) =x^3, y = -\frac{1}{4}f(x) -2 </code></p>
Similar Question 3
<p>The function <code class='latex inline'>y = x^3</code> has undergone each of the following sets of transformations. List three points on the resulting function.</p><p>eflected in the y-axis, vertically translated 45 units down</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 function <code class='latex inline'>y = x^3</code> has undergone each of the following sets of transformations. List three points on the resulting function.</p><p>reflected in the y-axis, horizontally stretched by a factor of 7, vertically translated 19 units down</p>
<p>Identify the parameters <code class='latex inline'>a, k, d</code>, and <code class='latex inline'>c</code> in the polynomial function <code class='latex inline'>\displaystyle y = \frac{1}{3}[-2(x + 3)]^4 </code></p><p>a) Describe how each parameter transforms the base function <code class='latex inline'>y =x^4</code></p><p>b) State the domain and range, the vertex, and the equation of the axis of symmetry of the transformed function.</p><p>c) Describe two possible orders in which the transformations can be applied to the graph of <code class='latex inline'>y = x^4</code> to produce the graph of <code class='latex inline'>\displaystyle y = \frac{1}{3}[-2(x + 3)]^4 -1 </code></p><p>d) Sketch graphs of the base function and the transformed function on the same set of axes.</p>
<p><code class='latex inline'>\displaystyle y=x^{3} </code> is stretched horizontally by a factor of 2, and then translated horizontally 3 units to the right. What is the equation of the resulting graph?</p><p>a) <code class='latex inline'>\displaystyle y=(2(x+3))^{3} \quad </code> c) <code class='latex inline'>\displaystyle y=\left(\frac{1}{2}(x-3)\right)^{3} </code></p><p>b) <code class='latex inline'>\displaystyle y=\left(\frac{1}{2} x\right)^{3}-3 </code></p><p>d) <code class='latex inline'>\displaystyle y=(2 x-3)^{3} </code></p>
<p>What is the relationship between <code class='latex inline'>y = x^3</code> and the graph of <code class='latex inline'>y = a(x -3)^3 + k</code>.</p>
<p>The function <code class='latex inline'>y = x^3</code> has undergone each of the following sets of transformations. List three points on the resulting function.</p><p>eflected in the y-axis, vertically translated 45 units down</p>
<p>For the graph, do the following..</p> <ul> <li>i) State whether the corresponding function has even degree or odd degree.</li> <li>ii) State whether the leading coefficient is positive or negative.</li> <li>iii) State the domain and range.</li> <li>iv) Describe the end behaviour.</li> <li>v) Identify the type of symmetry.</li> </ul> <img src="/qimages/6587" />
<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/24518" />
<p>Transformations are applied to <code class='latex inline'>y = x^3</code> to obtain the graph shown. Determine its equation.</p><img src="/qimages/6597" />
<p>Describe the similarities and differences between the parabola <code class='latex inline'>y = x^2</code> and power functions with even degree greater than two. </p>
<p>The function <code class='latex inline'>y = x^3</code> has undergone each of the following sets of transformations. List three points on the resulting function</p><p>reflected in the x-axis, horizontally compressed by a factor of <code class='latex inline'>\frac{7}{10}</code> , horizontally translated 12 units to the right, vertically translated 6 units up</p>
<p>Consider the graph below.</p> <ul> <li>i. Does it represent a power function of even degree? odd degree? Explain.</li> <li>ii. State the sign of the leading coefficient. Justify your answer.</li> <li>iii. State the domain and range.</li> <li>iv. Identify any symmetry.</li> <li>v. Describe the end behaviour.</li> </ul> <img src="/qimages/98" />
<ul> <li>i) 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. Then, write the corresponding equation.</li> <li>ii) State the domain and range of the transformed function. For even functions, state the vertex and the equation of the axis of symmetry.</li> </ul> <p><code class='latex inline'>\displaystyle f(x) =x^4, y = 5f[\frac{2}{5}(x -3)] + 1 </code></p>
<p>Consider the graph below.</p> <ul> <li>i. Does it represent a power function of even degree? odd degree? Explain.</li> <li>ii. State the sign of the leading coefficient. Justify your answer.</li> <li>iii. State the domain and range.</li> <li>iv. Identify any symmetry.</li> <li>v. Describe the end behaviour.</li> </ul> <img src="/qimages/97" />
<p>The function <code class='latex inline'>y = x^3</code> has undergone each of the following sets of transformations. List three points on the resulting function.</p> <ul> <li>vertically stretched by a factor of 25, horizontally compressed by a factor of 5, 6 horizontally translated 3 units to the right</li> </ul>
<p>For the graph, do the following..</p> <ul> <li>i) State whether the corresponding function has even degree or odd degree.</li> <li>ii) State whether the leading coefficient is positive or negative.</li> <li>iii) State the domain and range.</li> <li>iv) Describe the end behaviour.</li> <li>v) Identify the type of symmetry.</li> </ul> <img src="/qimages/6586" />
<p>Determine the cubic function that is obtained from the parent function <code class='latex inline'>\displaystyle y=x^{3} </code> after each sequence of transformations.</p><p>translation up 3 units and to the left 2 units</p>
<p>Assign the following functions for below:</p><p><code class='latex inline'>\displaystyle \begin{array}{llll} &y=-x^5, y = \frac{2}{3}x^4, y= 4x^3, y = 0.2x^6 \\ \end{array} </code></p><p>a) Extends from quadrant 3 to quadrant 1</p><p>b) Extends from quadrant 2 to quadrant 4</p><p>c) Extends from quadrant 2 to quadrant 1</p><p>d) Extends from quadrant 3 to quadrant 4</p>
<ul> <li>i) Write an equation for the function that results from each set of transformations.</li> <li>ii) State the domain and range. For even functions, state the vertex and the equation of the axis of symmetry.</li> </ul> <p><code class='latex inline'>f(x) =x^4</code> is compressed vertically by a factor of <code class='latex inline'>\frac{3}{5}</code>, stretched horizontally by a factor of <code class='latex inline'>2</code>, reflected in the y-axis, and translated 1 unit up and 4 units to the left.</p>
<p>Determine the cubic function that is obtained from the parent function <code class='latex inline'>\displaystyle y=x^{3} </code> after each sequence of transformations.</p><p>vertical compression by a factor of <code class='latex inline'>\displaystyle \frac{1}{2} </code>, translation down 2 units</p>
<ul> <li>i) 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. Then, write the corresponding equation.</li> <li>ii) State the domain and range of the transformed function. For even functions, state the vertex and the equation of the axis of symmetry.</li> </ul> <p><code class='latex inline'>\displaystyle f(x) =x^3, y = -\frac{1}{4}f(x) -2 </code></p>
<ul> <li>i) Write an equation for the function that results from each set of transformations.</li> <li>ii) State the domain and range. For even functions, state the vertex and the equation of the axis of symmetry.</li> </ul> <p><code class='latex inline'>f(x) =x^4</code> is compressed vertically by a factor of <code class='latex inline'>\frac{3}{5}</code>, stretched horizontally by a factor of 2, reflected in the y-axis, and translated 1 unit up and 4 units to the left.</p>
<p>The function <code class='latex inline'>y = x^3</code> has undergone each of the following sets of transformations. List three points on the resulting function.</p>
<p>The function <code class='latex inline'>y =x^3</code> has been vertidcally stretched by a factor of 5, horizontally compressed by a factor of <code class='latex inline'>\frac{1}{2}</code>, horizontally translated 21 units to the right, and vertically translated 4 units up.</p><p>a) Write the equation of the transformed function.</p><p>b) The point <code class='latex inline'>(1, 1)</code> is on the parent function. Determine the new coordinates of the transformed function.</p>
<p>Given the base function <code class='latex inline'>f(x) = x^4</code>, use a table of values or a graphing calculator to sketch a graph of <code class='latex inline'>y = f(x)</code>.</p>
<p>The function <code class='latex inline'>y = x^3</code> has undergone each of the following sets of transformations. List three points on the resulting function.</p><p>vertically stretched by a factor of 100, horizontally stretched by a factor of 2, vertically translated 14 units up</p>
<p>The function <code class='latex inline'>y = x^3</code> has undergone each of the following sets of transformations. List three points on the resulting function.</p><p>reflected in the x-axis, vertically compressed by a factor of <code class='latex inline'>\frac{6}{11}</code> , horizontally translated 11 5 units to the left, vertically translated 16 units up</p>
How did you do?
Found an error or missing video? We'll update it within the hour! 👉
Save videos to My Cheatsheet for later, for easy studying.