Precalculus Examples

$| x^{2} | + 4$

Step 1

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$x^{2} \geq 0$

Step 2

Since the left side has an even power, it is always positive for all real numbers.

All real numbers

Step 3

Since $x^{2}$ is never negative, the absolute value can be removed.

$x^{2} + 4$