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

1 Answer
Aug 17, 2015

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]}