# How do you find the domain and range of y=4absx?

Apr 18, 2017

$x \in \mathbb{R}$
$y \in \left[0 , + \infty\right)$

#### Explanation:

$\text{making a 'quick' sketch of the function will help}$

$\text{choose values of x and calculate y}$

$\textcolor{red}{x = 0} \to y = 4 | 0 | = 0 \to \left(0 , 0\right)$

$\textcolor{red}{x = 1} \to y = 4 | 1 | = 4 \to \left(1 , 4\right)$

$\textcolor{red}{x = 2} \to y = 4 | 2 | = 8 \to \left(2 , 8\right)$

$\textcolor{red}{x = - 1} \to y = 4 | - 1 | = 4 \to \left(- 1 , 4\right)$

$\textcolor{red}{x = - 2} \to y = 4 | - 2 | \to \left(- 2 , 8\right)$

$\text{plotting these points gives}$
graph{4|x| [-11.25, 11.24, -5.62, 5.635]}

$\text{from the graph we can see domain/range}$

$\text{domain is } x \in \mathbb{R}$

$\text{range is } \left[0 , + \infty\right)$