Age and Shoe Size

Question

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

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

Answer 1

To determine if the ordered pairs (x, y) form a function, we must check if every input (x value) corresponds to exactly one output (y value).

Looking at the data:

• For \( x = 8 \), there are two outputs: \( y = 7 \) and \( y = 9 \).
• For \( x = 9 \), there is one output: \( y = 8 \).
• For \( x = 10 \), there are two outputs: \( y = 9 \) and \( y = 10 \).
• For \( x = 14 \), there is one output: \( y = 9 \).
• For \( x = 15 \), there is one output: \( y = 11 \).
• For \( x = 33 \), there is one output: \( y = 9 \).
• For \( x = 27 \), there is one output: \( y = 9.5 \).
• For \( x = 45 \), there is one output: \( y = 10.5 \).

Since there are multiple y values corresponding to the same x values (specifically for x = 8 and x = 10), the data does not satisfy the definition of a function.

Therefore, the correct answer is:

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