Question

Discussion Topic
The group of points {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function, but the group of points {(1, 4), (2, 7), (3, 1), (5, 7)} is a function. What do you notice about the two groups of points? What do you think it means to be a function?

Answer 1

Notice that in the first group the x-value 0 appears twice, paired with two different y-values (1 and 5). In the second group every x-value (1, 2, 3, 5) appears only once.

A function is a relation that assigns exactly one output (y) to each input (x). That means no input x can be matched with two different outputs. So the first set is not a function because the input 0 has two different outputs; the second set is a function because each input has a single output.

(You can also check this visually: a set of points is a function if any vertical line would hit the graph at most once — the “vertical line test.”)