Final answer:
The graph of a function f(x) passes through the points (0,-2), (1,0), and (-1,0). The possible functions that could represent f(x) are y = -2, y = 0, and y = x².
Step-by-step explanation:
The graph of a function can pass through multiple points. In this case, the function f(x) passes through the points (0,-2), (1,0), and (-1,0). To determine which function could represent f(x), we can examine the behavior of the points. Since f(x) has a y-value of -2 when x=0, it means that f(0)=-2. Similarly, f(1)=0 and f(-1)=0. Based on these points, we can conclude that the function f(x) can be represented by either y = -2, y = 0, or y = x².