1. **Problem Statement:** Determine the domain and range for both $f(x)$ and its inverse from the given piecewise graph. 2. **Understanding Domain and Range:** - The **domain** of a function is the set of all possible input values ($x$-values). - The **range** is the set of all possible output values ($y$-values). - For the inverse function $f^{-1}(x)$, the domain and range swap compared to $f(x)$. 3. **Analyze $f(x)$ from the graph:** - Domain of $f(x)$: From $x=-4$ to $x=4$, so domain is $[-4,4]$. - Range of $f(x)$: The lowest $y$-value is $0$, highest is $4$, so range is $[0,4]$. 4. **Domain and range of inverse $f^{-1}(x)$:** - Domain of $f^{-1}(x)$ = Range of $f(x)$ = $[0,4]$. - Range of $f^{-1}(x)$ = Domain of $f(x)$ = $[-4,4]$. **Final answers:** - $\text{Domain of } f(x) = [-4,4]$ - $\text{Range of } f(x) = [0,4]$ - $\text{Domain of } f^{-1}(x) = [0,4]$ - $\text{Range of } f^{-1}(x) = [-4,4]$