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?
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 whether the ordered pairs (x, y) form a function, we need to check the definition of a function: for every input (x), there must be exactly one output (y).

Since I don't have access to the specific data you mentioned, I'll provide guidance on how to analyze it:

1. **Identify the x-values** (in this case, ages).
2. **Check if any x-value is associated with more than one y-value** (in this case, shoe sizes).

- If **any x-value** corresponds to **more than one y-value**, then the relation does not represent a function.
- If **every x-value** corresponds to **only one y-value**, then the relation represents a function.

Based on this reasoning:

- If you find that some x-values (ages) have multiple corresponding y-values (shoe sizes), the correct answer would be **D**: "No, because for some x's there are more than one y's."
- If each x-value has only one y-value, the correct answer would be **B**: "Yes, because for every x there is only one y."

Please analyze your data according to these criteria to choose the appropriate option.