Question

How can an absolute value function extend below the x-axis?

Answer 1

by translating or scaling the function

Explanation:

The parent absolute value function f(x) = |x| does not extend below the x-axis. The graph of a translated (and/or scaled) version of the function may extend below the x-axis.

In the attachment, one function has simply been translated down 3 (and right 2) so that it extends below the x-axis. The other one has been scaled by a negative number, so it does not go above the x-axis.