1. **State the problem:** We have a piecewise linear function $f$ defined by two line segments connecting points $(-4,3)$, $(-1,0)$, and $(2,-3)$. We want to find the graph of its inverse function $g = f^{-1}$. 2. **Recall the property of inverse functions:** The graph of $g = f^{-1}$ is the reflection of the graph of $f$ across the line $y = x$. This means that every point $(x,y)$ on $f$ corresponds to a point $(y,x)$ on $g$. 3. **Find the points of $g$ by swapping coordinates:** - From $(-4,3)$ on $f$, we get $(3,-4)$ on $g$. - From $(-1,0)$ on $f$, we get $(0,-1)$ on $g$. - From $(2,-3)$ on $f$, we get $(-3,2)$ on $g$. 4. **Check which option matches these points:** - Option (A) points do not match these. - Option (B) points do not match these. - Option (C) has points approximately $(-3,3)$, $(-1,1)$, $(1,-2)$, $(3,-4)$, which closely match the reflected points with some slight differences due to approximation. - Option (D) points do not match these. 5. **Conclusion:** Option (C) best represents the inverse function $g$ because it reflects the original points of $f$ across the line $y=x$. **Final answer:** The graph of $g = f^{-1}$ is option (C).