Question

Graph each function. State the domain and range.

$\mathit{f}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}\mathbf{\left|}\mathbf{x}\mathbf{\right|}$

Short answer

The domain is all real numbers and the range is non-negative real numbers i.e.,

$\mathbf{\{}\mathit{y}\mathbf{:}\mathit{y}\mathbf{\ge }\mathbf{0}\mathbf{\}}$

Step-by-step solution

Step 1. State the concept for absolute value function.

An absolute value function is a function that contains an algebraic expression within absolute value symbols. The absolute value of a number is its distance from 0 on the number line.

$f\left(x\right)=\left|x\right|=\left\{\begin{array}{c}x;x>0\\ -x;x\le 0\end{array}\right\}$

Step 2. Make a table for the given function.

Construct a table for$f\left(x\right)=\left|x\right|$by taking some values of $x$.

$x$	$y=f\left(x\right)=\left|x\right|$
$-2$	2
$-1$	1
0	0
1	1
2	2

Step 3. Plot the graph.

Plot the values of $x$and $f\left(x\right)$on a 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 $y$-coordinate values specify the range of the function. Since, the graph does not take any value less than or any negative value, the range is .