a. Yes, the graph represents a function because it passed the vertical line test.
b. Yes, the graph represents a function because it passed the vertical line test.
c. No, the graph does not represent a function because it failed the vertical line test.
In Mathematics, a vertical line test is a technique which is used to determine whether or not a given relation is a function.
According to the vertical line test, a vertical line must cut through the x-coordinate (x-axis) on the graph of a function at only one (1) point, in order for it to represent a function. Else, the relation does not represent a function because it can only have one output value (y) for a unique input value (x).
Part a and b.
Since each of the input values are uniquely mapped to an output value, it ultimately implies that the graph represents a function.
Part c.
In this context, we can reasonably and logically deduce that the relation in graph C correctly demonstrates an equation that is not a function because the vertical line passes through both point (0, 3) and point (0, -3).