Chapter 5: Q. 3 (page 282)

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.
True or False
To graph ${(x - 2)}^{3}$ , shift the graph of $y = x^{3}$ to the left $2$ units.

Short Answer

Expert verified

The statement is false, since the graph ${(x - 2)}^{3}$ should be graphed horizontally right to two unit.

Step by step solution

Step 1. Given

The graph $y = {(x - 2)}^{3}$

By shifting $y = x^{3}$ to left to two units.

Step 2. Horizontal shift.

If the argument $x$ of a function $f$ is replaced by $x + h, h > 0$ , the graph of the new function $y = f (x + h)$ is the graph of $f$ shifted horizontally left $h$ units.

If the argument $x$ of a function $f$ is replaced by $x - h, h > 0$ the graph of the new function $y = f (x - h)$ is the graph of $f$ shifted horizontally right $h$ units.

Step 3. Compare (x+h) with (x-2)

So the parent function is $y = x^{3}$

And the graph $y = {(x - 2)}^{3}$ is graphed by shifting horizontally the basic function right to two units.

So the given statement is false.

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Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.
True or False
To graph ${(x - 2)}^{3}$ , shift the graph of $y = x^{3}$ to the left $2$ units.

Short Answer

Step by step solution

Step 1. Given

Step 2. Horizontal shift.

Step 3. Compare (x+h) with (x-2)

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Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.True or FalseTo graph (x-2)3, shift the graph of y=x3to the left 2 units.

Short Answer

Step by step solution

Step 1. Given

Step 2. Horizontal shift.

Step 3. Compare (x+h) with (x-2)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.
True or False
To graph ${(x - 2)}^{3}$ , shift the graph of $y = x^{3}$ to the left $2$ units.