Q. 62 - Precalculus Enhanced with Graphing Utilities

Question

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 $y=5\left|x\right|$

?

Step-by-Step Solution

Answer

Graph of functions are 

Step 1. given data

The given functions are

$$\begin{gathered} y=\left|x\right| \\ y=2\left|x\right| \\ y=4\left|x\right| \\ y=\frac{1}{2}\left|x\right| \\ y=\frac{1}{4}\left|x\right| \\ y=5\left|x\right| \end{gathered}$$

Step 2. graph of the parent function

Plot the graph of the function $y=\left|x\right|$

Step 3. graph of the transformed function

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

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

Step 4. graph of the transformed function

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

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

Step 5. graph of the transformed function

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

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

Step 6. graph of the transformed function

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

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

Step 7. graph of the transformed function

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

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