Chapter EP, Problem 2.7.2EP

To determine

The type of function represented by each graph.

Answer to Problem 2.7.2EP

So, the required function is $y=-\left|x\right|+m$ .

Explanation of Solution

Given information:

The graph:

Formula used:

Multiplying function $f\left(x\right)$ with -1 mirrors the graph along x-axis.

Adding $a$ to a function $f\left(x\right)$ , moves the graph upward.

Comparing the graph with $y=\left|x\right|$

The graph of $y=\left|x\right|$ is,

Recall that Multiplying function $f\left(x\right)$ with -1 mirrors the graph along x-axis.

So, multiplying $-1$ to function $f\left(x\right)$

  $y=-\left|x\right|$

The graph of $y=-\left|x\right|$ is,

As we can see, the given graph is upward then $y=-\left|x\right|$ ,

Lets assume, the given graph is $m$ upward then $y=-\left|x\right|$ ,

Recall that Adding $a$ to a function $f\left(x\right)$ , moves the graph upward.

So, the required function is $y=-\left|x\right|+m$ .