Chapter 4.7, Problem 51E

To determine

Graph the function and describe the domain and range.

Answer to Problem 51E

Domain of the function is the set of all real numbers.

The range of the function is (0, $\infty$ ).

Explanation of Solution

Given information: $\begin{array}{l}f(x)=-x+2,\text{if}x\le -2\text{and}\\ f(x)=\left|x\right|,\text{if}x>-2.\end{array}$

Calculation:

The graph of the function is given below.

  

Domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis. So the domain of the above graph is $x\le -2\text{and}x>-2$ that is set of all real numbers.

It is clear from the graph for every real value of $x$ the value of $y$ lies between 0 and $\infty$ .

So, the range of the function is (0, $\infty$ ).