Given the graph below, which of the following statements is true?
a. the graph represents a one-to-one function because every x-value is paired with only one y-value.
b. the graph represents a one-to-one function because it is defined for all x-values.
c. the graph does not represent a one-to-one function because it does not pass through the origin.
d. the graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

To be a function, it has to pass the vertical line test, which means a vertical line drawn anywhere in the graph should cut the graph only once, not more.

To be a one-to-one function, it has to pass the vertical line test as well as the horizontal line test, which means that a horizontal line drawn anywhere in the graph should cut the graph only once, not more.

Of course, it passes the vertical line test, so its a function.

Does it pass the horizontal line test? NO! As shown in the attached picture, the blue line (horizontal line) cuts the graph at 3 places. We therefore eliminate choices A and B. We can eliminate choice C because nowhere is it required a function to pass through the origin for it to be one-to-one. Hence, the answer is D (blue line shows this).

ANSWER: D