3.4 Transformation of Cubic and Quartic Functions
Chapter
Chapter 3
Section
3.4
Lectures 5 Videos
Solutions 40 Videos

Match each equation with the most suitable graph.

• (a) f(x) = 2(x + 1)^2 + 1
• (b) g(x) = -\frac{1}{3}(x +1)^3 - 1
• (c) y = 0.2(x -4)^4 -3
• (d) y = -1.5(x + 3)^4 +4
0.31mins
Q1

State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function.

\displaystyle f(x) =\frac{5}{4}x^4 +3 

1.42mins
Q2a

State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function.

\displaystyle g(x) = 3x -4 

0.49mins
Q2b

State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function.

\displaystyle y = (3x +4)^3 - 7 

2.04mins
Q2c

State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function.

\displaystyle y = -(x + 8)^4 

1.05mins
Q2d

State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function.

\displaystyle y = -4.8(x - 3)(x -3) 

1.29mins
Q2e

State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function.

\displaystyle y = 2(\frac{1}{5}x + 7)^3 -4 

1.57mins
Q2f

Describe the transformations that were applied to the parent function to create each of the following graphs. Then write the equation of the transformed function.

1.09mins
Q3a

Describe the transformations that were applied to the parent function to create each of the following graphs. Then write the equation of the transformed function.

1.26mins
Q3b

Describe the transformations that were applied to the parent function to create each of the following graphs. Then write the equation of the transformed function.

1.29mins
Q3c

Describe the transformations that were applied to the parent function to create each of the following graphs. Then write the equation of the transformed function.

1.14mins
Q3d

Describe the transformations that were applied to y = x^3 to create each of the following functions.

\displaystyle y = 12(x - 9)^3 - 7 

0.54mins
Q4a

Describe the transformations that were applied to y = x^3 to create each of the following functions.

\displaystyle y = (\frac{7}{8}(x +1))^3 + 3 

1.30mins
Q4b

Describe the transformations that were applied to y = x^3 to create each of the following functions.

\displaystyle y = -2(x -6)^3 - 8 

1.13mins
Q4c

Describe the transformations that were applied to y = x^3 to create each of the following functions.

\displaystyle y = (x + 9)(x + 9)(x +9) 

0.37mins
Q4d

Describe the transformations that were applied to y = x^3 to create each of the following functions.

\displaystyle y = -2(-3(x - 4))^3 -5 

1.57mins
Q4e

Describe the transformations that were applied to y = x^3 to create each of the following functions.

\displaystyle y = (\frac{3}{4}(x -10))^3 

0.59mins
Q4f

For each graph, determine the equation of the function in the form y = a(x - h)^2 + k. Then describe the transformations that were applied to y = x^2 to obtain each graph.

1.25mins
Q5a

For each graph, determine the equation of the function in the form y = a(x - h)^2 + k. Then describe the transformations that were applied to y = x^2 to obtain each graph.

1.37mins
Q5b

The function y = x^3 has undergone the following sets of transformations. If y= x^3 passes through the points (-1, -1), (0, 0), and (2, 8), list the coordinates of these transformed points on each new curve. Show your work.

vertically compressed by a factor of \frac{1}{2}, horizontally compressed by \frac{1}{5} a factor of 5, and horizontally translated 6 units to the left

1.09mins
Q6a

The function y = x^3 has undergone the following sets of transformations. If y= x^3 passes through the points (21, 21), (0, 0), and (2, 8), list the coordinates of these transformed points on each new curve.

reflected in the y-axis, horizontally stretched by a factor of 2, and vertically translated 3 units up

0.49mins
Q6b

The function y = x^3 has undergone the following sets of transformations. If y= x^3 passes through the points (-2, -8), (0, 0), and (2, 8), list the coordinates of these transformed points on each new curve.

reflected in the x-axis, vertically stretched by a factor of 3, horizontally translated 4 units to the right, and vertically translated \frac{1}{2} of a unit down

1.04mins
Q6c

The function y = x^3 has undergone the following sets of transformations. If y= x^3 passes through the points (21, 21), (0, 0), and (2, 8), list the coordinates of these transformed points on each new curve.

vertically compressed by a factor of \frac{1}{10}, horizontally stretched by a factor of 7, and vertically translated 2 units down

0.48mins
Q6d

The function y = x^3 has undergone the following sets of transformations. If y= x^3 passes through the points (21, 21), (0, 0), and (2, 8), list the coordinates of these transformed points on each new curve.

reflected in the y-axis, reflected in the x-axis, and vertically translated \frac{9}{10} of a unit up

0.49mins
Q6e

The function y = x^3 has undergone the following sets of transformations. If y= x^3 passes through the points (21, 21), (0, 0), and (2, 8), list the coordinates of these transformed points on each new curve.

horizontally stretched by a factor of 7, horizontally translated 4 units to the left, and vertically translated 2 units down

0.47mins
Q6f

The graph shown is a result of transformations applied to y = x^4 Determine the equation of this transformed function.

1.19mins
Q7

Dillan has reflected the function g(x) = x^3 in the x-axis, vertically A compressed it by a factor of \displaystyle \frac{2}{3}, horizontally translated it 13 units to the right, and vertically translated it 13 units down. Three points on the resulting curve are \displaystyle(11, -\frac{23}{3}), (13, -13), and \displaystyle(15, -\frac{55}{3}).

Determine the original coordinates of these three points on g(x).

2.52mins
Q8

Determine the x-intercepts of each of the following polynomial functions. Round to two decimal places, if necessary.

 \displaystyle y = 2(x +3)^4 -2 

0.34mins
Q9a

Determine the x-intercepts of each of the following polynomial functions. Round to two decimal places, if necessary.

 \displaystyle y = (x -2)^3 - 8 

0.18mins
Q9b

Determine the x-intercepts of each of the following polynomial functions. Round to two decimal places, if necessary.

 \displaystyle y = -3(x + 1)^3 + 48 

0.32mins
Q9c

Determine the x-intercepts of each of the following polynomial functions. Round to two decimal places, if necessary.

 \displaystyle y = -5(x + 6)^4 -10 

0.42mins
Q9d

Determine the x-intercepts of each of the following polynomial functions. Round to two decimal places, if necessary.

 \displaystyle y = 4(x - 8)^4 -12 

0.30mins
Q9e

Determine the x-intercepts of each of the following polynomial functions. Round to two decimal places, if necessary.

 \displaystyle y = -2(2x + 5)^3 - 20 

0.40mins
Q9f

Consider the function y = 2(x - 4)^n + 1, n \in \mathbb{N}.

How many zeros will the function have if n = 3? Explain how you know.

0.17mins
Q10a

Consider the function y = 2(x - 4)^n + 1, n \in \mathbb{N}.

How many zeros will the function have if n = 4? Explain how you know.

0.12mins
Q10b

For what values of n will the reflection of the function y = x^n in the x-axis be the same as its reflection in the y-axis. Explain your reasoning.

0.50mins
Q11a

For what values of n will the reflection of the function y = x^n in the x-axis be the same as its reflection in the y-axis. Explain your reasoning.

For what values of n will the reflections be different? Explain your

0.36mins
Q11b

What transformations are required on the function y = (x- 4)(x + 1)(x - 8) to create the function y = 2(x -1)(x + 4)(x - 5)? Show your work.

The function f(x) = x^2 was transformed by vertically stretching it, horizontally compressing it, horizontally translating it, and vertically translating it. The resulting function was then transformed again by reflecting it in the x-axis, vertically compressing it by a factor of \frac{4}{5}, horizontally compressing it by a factor of \frac{1}{2}, and vertically translating it 6 units down. The equation of the final function is f(x) = -4(4(x + 3))^2 - 5. What was the equation of the function after it was transformed the first time?