Which of the following equations represents a relation that is not a function?

A relation is defined as a function if every input (or x-value) corresponds to exactly one output (or y-value). When examining the given options, we can identify which relation fails this criterion.

For the equation x = y^2, this represents a parabola that opens to the right. For any positive value of x, there are typically two corresponding values of y — one positive and one negative (since both (y) and (-y) yield the same (y^2)). For instance, if x is 4, y could be 2 or -2. Because of this characteristic, multiple values of y correspond to a single value of x, which means that this relation does not meet the definition of a function.

On the other hand, the equations y = x^2, y = x^3, and sqrt(x) do define functions because each x-value produces one and only one corresponding y-value. The equation y = x^2 results in a parabola that opens upwards, y = x^3 is a cubic function that passes through the origin, and sqrt(x) provides positive outputs for non-negative x-values. Each of these equations establishes a consistent rule that assigns a single output to every