Chapter 4: Q. 5 (page 245)

In Problems 5, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.
$f (x) = (x + 2)^{3}$

Short Answer

Expert verified

The graph is shown below:

Step by step solution

Given information

The given function is $f (x) = (x + 2)^{3}$ .

Graph the base function

To help establish the graph, find the points at $x = - 2, x = 0$ and $x = 2$ .

$\begin{array}{rcl} y & = & {(- 2)}^{3} \\ = & 8 \\ y & = & {(0)}^{3} \\ = & 0 \\ y & = & {(2)}^{3} \\ = & 8 \end{array}$

The graph is shown below:

Graph the given function

Shift the previous graph $2$ units to the left to get the desired graph for the given function $f (x)$ .

To help establish the graph, determine three points by subtracting 2 from the $x$ -coordinates of the points in step 2.

Maintain the $y$ -coordinates of these points.

The given function graph is shown below:

Write the conclusion

The graph of the given function is shown below:

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In Problems 5, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.
$f (x) = (x + 2)^{3}$

Short Answer

Step by step solution

Given information

Graph the base function

Graph the given function

Write the conclusion

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Study anywhere. Anytime. Across all devices.

In Problems 5, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.f(x)=(x+2)3

Short Answer

Step by step solution

Given information

Graph the base function

Graph the given function

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

In Problems 5, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.
$f (x) = (x + 2)^{3}$