Math Snap

STEP 1

Assumptions1. The function is piece-wise defined with three parts $0$ for $x \leq -4$, $-x$ for $-4 \leq x <0$, and $x^{}$ for $x \geq0$.

STEP 2

First, we need to determine the range of each piece of the function separately.For $x \leq -4$, the function is constant at $0$. So, the range for this part is just $0$.

STEP 3

For $- \leq x <0$, the function is $-x$. As $x$ increases from $-$ to $0$, $-x$ decreases from $$ to $0$. So, the range for this part is $[0,)$.

STEP 4

For $x \geq0$, the function is $x^{2}$. As $x$ increases from $0$ to $\infty$, $x^{2}$ also increases from $0$ to $\infty$. So, the range for this part is $[0, \infty)$.

Now, we combine the ranges of all the pieces to get the range of the entire function.
The range of the function $f(x)$ is the set of all possible values of $f(x)$, which is the union of the ranges of all the pieces.
So, the range of $f(x)$ is $[0, \infty)$.