# How do you graph f(x) = |3x - 2|?

Oct 2, 2017

Basically, you draw the graph f(x)=|3x−2|, and then reflect everything below the y-axis up:

graph{|3x-2| [-10, 10, -5, 5]}

#### Explanation:

When graphing absolute value graphs, it's important you either graph by hand or visualise the function without the absolute values.

In this case, the function without the absolute value is f(x)=3x−2.

graph{3x-2 [-10, 10, -5, 5]}

A property of absolute values is that they make negative values into positive values.

This is what happens in a function with an absolute value, where every negative x-value (i.e. everything below the y-axis) is reflected upwards (i.e. reflected horizontally over the y-axis).

So the graph of f(x)=|3x−2| looks like this:

graph{|3x-2| [-10, 10, -5, 5]}

Another way you could graph this is by finding the x- and y-intercepts, and remembering that absolute value graphs make a V-shape:

x-intercept (when y=0):
0=|3x−2|
$3 x = 2$
$\therefore$ $x = \frac{2}{3}$

y-intercept (when x=0):
y=|3(0)−2|
y=|−2|
$\therefore$ $y = 2$

Overall, graphing simpler types of absolute value equations is best done by first graphing the original equation, and then reflecting the negative values up.