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Q. 6

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Found in: Page 112

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

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

The given statement is true.

See the step by step solution

## Step 1. Given Information

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

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 $y=f\left(x\right),$ the graph of the new function $y=f\left(x\right)+k$ 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 $f\left(x\right)={x}^{3}+5$ is the graph of function shifted vertically up $5$units.

Therefore, the statement is true.