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Q. 62

Expert-verified
Found in: Page 103

### Precalculus Enhanced with Graphing Utilities

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

# Graph $y=\left|x\right|$ . Then on the same screen graph $y=2\left|x\right|$, followed by $y=4\left|x\right|$, followed by $y=\frac{1}{2}\left|x\right|$.What pattern do you observe? Can you predict the graph of$y=\frac{1}{4}\left|x\right|$? of $y=5\left|x\right|$?

Graph of functions are

See the step by step solution

## Step 1. given data

The given functions are

$y=\left|x\right|\phantom{\rule{0ex}{0ex}}y=2\left|x\right|\phantom{\rule{0ex}{0ex}}y=4\left|x\right|\phantom{\rule{0ex}{0ex}}y=\frac{1}{2}\left|x\right|\phantom{\rule{0ex}{0ex}}y=\frac{1}{4}\left|x\right|\phantom{\rule{0ex}{0ex}}y=5\left|x\right|$

## Step 2. graph of the parent function

Plot the graph of the function $y=|x|$

## Step 3. graph of the transformed function

Plot the graph of the function $y=2|x|$ on the same Cartesian plane

graph of $y=2|x|$ is equivalent to the vertically stretched graph of $y=|x|$ by the factor $2$

## Step 4. graph of the transformed function

Plot the graph of the function $y=4|x|$on the same Cartesian plane

graph of $y=4|x|$ is equivalent to the vertically stretched graph of $y=|x|$ by the factor $4$

## Step 5. graph of the transformed function

Plot the graph of the function$y=\frac{1}{2}|x|$on the same Cartesian plane

graph of $y=\frac{1}{2}|x|$ is equivalent to the vertically compressed graph of$y=|x|$ by the factor$\frac{1}{2}$

## Step 6. graph of the transformed function

Plot the graph of the function$y=\frac{1}{4}|x|$ on the same Cartesian plane

graph of $y=\frac{1}{4}|x|$ is equivalent to the vertically compressed graph of$y=|x|$ by the factor$\frac{1}{4}$

## Step 7. graph of the transformed function

Plot the graph of the function$y=5|x|$ on the same Cartesian plane

graph of $y=5|x|$ is equivalent to the vertically stretched graph of $y=|x|$ by the factor $5$