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

1 Answer
Aug 17, 2015

Answer:

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]}