Explain why the vertical line test is used to determine if a graph represents a function.

A function can only have one y value for each value of x, ie., y = f(x). The vertical line test verifies this. If you move a vertical line across the grid, your graph should never intersect this line at more than one place at a time. If it intersects at 2 or more places, there is no way a y=f(x) can make this happen, so then it is not a function.