Answer: B) This is a graph of a function, but it's not one-to-one.
Explanation:
We have a function because this graph passes the vertical line test. It is impossible to draw a single vertical line to have it pass through more than one point on the V shaped curve. Any x input leads to exactly one y output.
Even though we have a function, it is not one-to-one. Note how the curve fails the horizontal line test. It is possible to draw a horizontal line and have it pass through more than one point on the curve.
For example, draw a horizontal line through y = 3 and it passes through (-3,3) and (3,3) simultaneously. A one-to-one function is where any y output corresponds to exactly one x input, and vice versa. The output y = 3 corresponds to two different inputs x = -3 and x = 3 at the same time.
Why do we care about one-to-one functions? Well it's to help set up the inverse. The inverse goes the opposite direction of what the original function does. In this case, this function doesn't have an inverse unless we restrict the domain in some way.
