Solution assignment 04 Absolute value |x|

Draw the graph of $f(x)=|x^2-1|$

We apply the definition of the absolute value.

$|x^2-1|=x^2-1$ if $x^2-1\geq0$ , so if $x\leq-1$ or $x\geq1$

$|x^2-1|=-(x^2-1)=-x^2+1$ if $x^2-1<0$ , so if $-1<x<1$

This results in the following graph making use of the knowledge of quadratic functions.