Chapter EP, Problem 2.6.6EP

To determine

To find:The graph, domain and range of the function.

Answer to Problem 2.6.6EP

The graph is absolute value function, domain is real numbers and the range is non negative real numbers.

Explanation of Solution

Given:

The function is given as,

  $h\left(x\right)=\left|x\right|-3$

Calculation:

The values for various x are tabulated below:

x	h ( x )
-2	-1
-1	-2
0	-3
1	-2
2	-1

The range of $h\left(x\right)=\left|x\right|-3$ is $\left\{-1,-2,-3\right\}$

The domain of $h\left(x\right)=\left|x\right|-3$ is $\left\{-2,-1,0,1,2\right\}$

The graph is plotted as,

Thus, the graph is absolute value function, domain is real numbers and the range is non negative real numbers.