Chapter 2.4, Problem 62AYU

In Problems 64-71, use a graphing utility.

Exploration 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 $y=5\left|x\right|$?

To determine

To graph: Graph the equations $y = \left|x\right|, y = 2\left|x\right|, y = 4\left|x\right|$ and $y = \frac{1}{2}\left|x\right|$. Then observe the pattern from the graph drawn. Predict the graph of $y = \frac{1}{4}\left|x\right|$ and $y = 5\left|x\right|$

Answer to Problem 62AYU

Explanation of Solution

To sketch:

Graph the following equation with the graphing utility:

1. $y = \left|x\right|$

2. $y = 2\left|x\right|$

3. $y = 4\left|x\right|$

4. $y = \frac{1}{2}\left|x\right|$

Interpretation:

The equation $y = \left|x\right|$ is an absolute value line with the vertex point $\left(0, 0\right)$. Multiplying the values 2 and 4 with $\left|x\right|$ gives the shrinks absolute value line. And dividing the value by 2 gives the extended absolute value line.

Therefore, the equation $y = \frac{1}{4}\left|x\right|$ gives the extended absolute value and the equation $y = 5\left|x\right|$ gives the shrinks absolute value line.

That is, the graph must be like follows: