Range Math Example 3

Solution

1. 1
   Since $|x| \geq 0$, we have $-|x| \leq 0$, so $f(x) = -|x| + 4 \leq 4$.
2. 2
   The maximum value is $4$ (at $x = 0$), and $f(x) \to -\infty$ as $|x| \to \infty$. The range is $(-\infty, 4]$.