Question

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

Answer 1

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|`
`3x=2`
`therefore` `x=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.