1. The problem asks to identify which curve could be the sketch of the function $y=f(x)$. 2. Recall that a function $f(x)$ assigns exactly one output $y$ for each input $x$. This means the graph of a function must pass the vertical line test: any vertical line should intersect the graph at most once. 3. Analyze each graph: - Graph A: An ellipse centered near the origin. Vertical lines intersect an ellipse twice in some regions, so it fails the vertical line test. Not a function. - Graph B: A sideways parabola opening leftward. Vertical lines intersect it twice in some regions, so it fails the vertical line test. Not a function. - Graph C: A piecewise linear graph with a corner near the origin, going downward to the right and upward to the left. Vertical lines intersect it once at most. Passes the vertical line test. Could be a function. - Graph D: A piecewise linear graph with two horizontal line segments connected by a sloping segment. Vertical lines intersect it once at most. Passes the vertical line test. Could be a function. 4. Since the problem asks which curve could be the graph of a function, the answer is either Graph C or Graph D. 5. Without more information, both C and D satisfy the function criteria, but typically piecewise linear graphs with corners and no vertical overlaps are functions. Final answer: Graph C or Graph D could be the graph of the function $y=f(x)$.