Chapter 2: Q. 6 (page 112)

True or False
To obtain the graph of $f (x) = x^{3} + 5,$ shift the graph of $y = x^{3}$ vertically up $5$ units.

Short Answer

Expert verified

The given statement is true.

Step by step solution

Step 1. Given Information

There is the graph of $f (x) = x^{3} + 5 .$

We have to tell whether the statement is true or false if we shift the graph of $y = x^{3}$ vertically up $5$ units.

Step 2. Analyze the graph

The concept is if a positive real number k is added to the outputs of a function $y = f (x),$ the graph of the new function $y = f (x) + k$ is the graph of f shifted vertically up k units.

So, if $5$ is added to the outputs of a function $y = x^{3}$ , the graph of the new function $f (x) = x^{3} + 5$ is the graph of function shifted vertically up $5$ units.

Therefore, the statement is true.

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True or False
To obtain the graph of $f (x) = x^{3} + 5,$ shift the graph of $y = x^{3}$ vertically up $5$ units.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Analyze the graph

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True or FalseTo obtain the graph of f(x)=x3+5,shift the graph of y=x3vertically up 5units.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Analyze the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

True or False
To obtain the graph of $f (x) = x^{3} + 5,$ shift the graph of $y = x^{3}$ vertically up $5$ units.