Chapter EP, Problem 2.6.9EP

To determine

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

Answer to Problem 2.6.9EP

The graph is piecewise function, domain is real numbers and the range is $\left\{y|y<-2\text{ or }y=4\right\}$ .

Explanation of Solution

Given:

The function is given as,

  $h\left(x\right)=\left\{\begin{array}{l}x\text{ if }x<-2\\ \text{4 if }x\ge -2\end{array}\right\}$

Calculation:

The values for various x are tabulated below:

x	h ( x )
-2	-2
--3	-3
-4	-4

The graph is plotted as,

The function $h\left(x\right)=x$ for $x<-2$ , stops with an open circle and does not satisfy the inequality.

The function $h\left(x\right)=x$ for $x\ge 2$ , begins with an open circle and does satisfy the inequality.

Hence, the range is $\left\{y|y<-2\text{ or }y=4\right\}$ .

Thus, the graph is piecewise function, domain is real numbers and the range is $\left\{y|y<-2\text{ or }y=4\right\}$ .