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

Aug 17, 2015

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

#### Explanation:

If $x = 1 \mathmr{and} x = - 1 \to f \left(x\right) = 0$

For all values in between:
$- 1 < x < 1 \to {x}^{2} - 1 < 0$
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:
$f \left(x\right) = - {x}^{2} + 1$

Outside of this the function the bars have no effect:
$f \left(x\right) = {x}^{2} - 1$

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