Chapter 3.7, Problem 3GP

To determine

To graph the function and find the domain and range.

Explanation of Solution

Given:

Function:

  $f(x)=\{\begin{array}{l}2x+1\text{ if }x>0\\ \text{3 if }x\le \text{0}\end{array}$

Calculation for graph:

Consider,

  $f(x)=\{\begin{array}{l}2x+1\text{ if }x>0\\ \text{3 if }x\le \text{0}\end{array}$

Here, substitute different values for x.

For x > 0, the function is f ( x ) = 2x + 3.

Values of x	Values of f (x)
0	3
1	5
-1	1
2	7
-2	-1

By taking different values of x , the graph can be plotted.

For $x\le 0$ , the function is $f(x)=3$ .

Values of x	Values of f (x)
-1	3
-2	3
-3	3
-4	3
-5	3

By taking different values of x , the graph can be plotted.

Graph:

  

Interpretation:

Domain of a function is where the function is defined on a graph.

From the graph,

The function is defined at all the points. Therefore, the domain of the graph is $(-\infty ,\infty )$ for all the values of x .

Also, the range is the set of all values that a function passes through. It is the coordinate pair.

From the graph,

Therefore, the range of the function is $[3,\infty )$ .