Chapter EP, Problem 2.6.10EP

To determine

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

Answer to Problem 2.6.10EP

The graph is piecewise function, domain is real numbers and the range is $\left\{y|y>1\text{ or }y=-3\right\}$ .

Explanation of Solution

Given:

The function is given as,

  $f\left(x\right)=\left\{\begin{array}{l}-3\text{ if }x\le 1\\ \text{-x if }x>1\end{array}\right\}$

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 $f\left(x\right)=-x$ for $x>1$ , stops with an open circle and does not satisfy the inequality.

The function $f\left(x\right)=-3$ for $x\le 1$ , begins with an open circle and does satisfy the inequality.

Hence, the range is $\left\{y|y>1\text{ or }y=-3\right\}$ .

Thus, the graph is piecewise function, domain is real numbers and the range is $\left\{y|y>1\text{ or }y=-3\right\}$ .