Question

How do you graph `f(x) =abs(x^2-1)`?

Answer 1

With absolute you combine graphs, depending on the values between the bars.

Explanation:

If `x=1orx=-1->f(x)=0`

For all values in between:
`-1 < x<1->x^2-1<0`
and the bars have to do their work and flip the signs, so the part that would be under the `x`-axis is mirrored upward:
`f(x)=-x^2+1`

Outside of this the function the bars have no effect:
`f(x)=x^2-1`

At the points `(-1,0)and(1,0)` these two functions meet:
graph{|x^2-1| [-6.846, 8.954, -1.48, 6.42]}