# How do you graph y=4absx using a table?

Mar 21, 2018

#### Explanation:

Using a table for a function is the simplest way to find out roughly $5$ key points to get a general idea of how a function works.

Remember, when using an absolute value function, our $y$ values will always be positive, due to the conditions $| x |$

Since there are no horizontal shifts, it's a good idea to get two points left of the vertex, and right of the vertex, which is the origin $\left(0 , 0\right) :$

$f \left(- 2\right) = 4 | - 2 | \text{ becomes } f \left(- 2\right) = 4 \left(2\right) = \textcolor{b l u e}{8}$
$f \left(- 1\right) = 4 | - 1 | \text{ becomes } f \left(- 2\right) = 4 \left(1\right) = \textcolor{b l u e}{4}$
$f \left(0\right) = 4 | - 0 | \text{ becomes } f \left(- 2\right) = 4 \left(0\right) = \textcolor{b l u e}{0}$
$f \left(1\right) = 4 | 1 | \text{ becomes } f \left(- 2\right) = 4 \left(1\right) = \textcolor{b l u e}{4}$
$f \left(2\right) = 4 | 2 | \text{ becomes } f \left(- 2\right) = 4 \left(2\right) = \textcolor{b l u e}{8}$