Provide an appropriate response.Why does the horizontal line test (checking if a function is one-to-one) work?

Question

What will be an ideal response?

Answer 1

Answers may vary. One possibility: any two points that lie on the same horizontal line have the same y-coordinate. Thus, if any horizontal line intersects the graph of the function more than once, this would indicate that two different x-coordinates correspond to the same y-coordinate (and thus two ordered pairs have the same y-coordinate). Such a function cannot be one-to-one. However, if no two ordered pairs have the same y-coordinate, then the function is one-to-one.