Question

What is the graph of the absolute value function `f(x) = 4 | x | – 2`?

Answer 1

The graph of `f(x)` is the standard "V" graph of `absx` scaled by 4 units and shifted 2 units negative ("down") on the `y-`axis.

Explanation:

`f(x) =4absx-2`

Let's first consider the "parent" graph `y=absx`

This is the standard "V" graph shown below:

graph{absx [-10, 10, -5, 5]}

Now, `f(x)` is this standard graph scaled by 4 units and shifted 2 units negative ("down") on the `y-`axis. As below:

graph{4absx-2 [-10, 10, -5, 5]}