Chapter 4.7, Problem 7CYU

To determine

To Graph :

Graph the function and state the domain and range.

Answer to Problem 7CYU

Domain is all real numbers.

Range = $\{y:y>3\}$

Explanation of Solution

Given Information:

Given equation is :

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

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 :

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

Here both the functions are linear

x	$x>-1$	$x\le -1$	$y=f(x)=\{\begin{array}{l}2x-1;x>-1\\ -x;x\le -1\end{array}$
-3	No	Yes	3
-2	No	Yes	2
-1	No	Yes	1
0	Yes	No	-1
1	Yes	No	1

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 or equal to y = -3 , the range is = $\left\{y:y>-3\right\}$