Question

Oliver is doing a study on age and shoe size. He has collected the data shown above. Do the ordered pairs (x, y) he has collected form a function?

x (age) y (size)
8 7
9 8
10 9
8 9
14 9
15 11
10 10
33 9
27 9.5
45 10.5

A) Cannot be determined
B) Yes, because for every x there is only one y.
C) Yes, because for every y there is only one x.
D) No, because for some x's there are more than one y's.

Answer 1

D

Explanation:

The definition of a function states that for every x there is only one y. If you look at the data table for an x- value of 8 there are 2 different y-values 7 and 9. Therefore the correct answer is No, because for some x's there are more than one y's.

Answer 2

Answer: D) No, because for some x's there are more than one y's.

Explanation:

By the definition of function,

In a function For the every input there is a single value of output.

That is, if F is a function such that
`F(x_1) \\eq F(x_2)`

Then,
`x_1` and
`x_2` must be distinct.

But according to the given table,

For the value of 8 there are two outputs values 7 and 9.

Therefore, we can say that the given ordered pairs (x, y) can not make the function because there are more than on y's for one value of x's.