Short Answer

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

The given statement is true.

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Step by Step Solution

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TABLE OF CONTENTS

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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Short Answer

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

Step by Step Solution

Step 1. Given Information

Step 2. Analyze the graph

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Precalculus Enhanced with Graphing Utilities

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Short Answer

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

Step by Step Solution

Step 1. Given Information

Step 2. Analyze the graph

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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.