Chapter 4.7, Problem 25PPS

To determine

To Graph :

Graph the function and state the domain and range.

Answer to Problem 25PPS

Domain is all real numbers.

Range = $\{y:y\ge -3\}$

Explanation of Solution

Given Information:

Given equation is :

  $y=f(x)=\{\begin{array}{l}\frac{1}{2}x-1;x>3\\ -2x+3;x\le 3\end{array}$

Calculation :

This is a piece-wise defined function . Make a table for different value in the domain and include the values for which the function changes :

  $y=f(x)=\{\begin{array}{l}\frac{1}{2}x-1;x>3\\ -2x+3;x\le 3\end{array}$

Here both the functions are linear

x	$x>3$	$x\le 3$	$y=f(x)=\{\begin{array}{l}\frac{1}{2}x-1;x>3\\ -2x+3;x\le 3\end{array}$
1	No	Yes	1
2	No	Yes	-1
3	No	Yes	-3
4	Yes	No	1
5	Yes	No	1.5

Plotting the values and joining, we get the required graph :

  

The x -coordinate values specify the domain of the function . Since the graph covers all possible values of x , the domain is all real numbers.

The y -coordiante values specify the range of the function . Since , the graph does not take any value less than y = -3 , the range is = $\left\{y:y\ge -3\right\}$