Question

For each of the relations below, determine which represent functions. Select all that apply.
(2 points)
Responses

{(0,-1), (3,6),(6,8),(9,12),(0,-1)}








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Answer 1

To determine whether a relation is a function, each input (or x-value) in the relation must be associated with exactly one output (or y-value).

Let's examine the relation you provided:

\[
\{(0,-1), (3,6),(6,8),(9,12),(0,-1)\}
\]

In this relation, the x-values are:
- 0 (which appears twice, with the same y-value of -1)
- 3
- 6
- 9

All x-values are unique with the exception of the 0, which still maps to the same y-value (-1). Since each x-value is associated with exactly one y-value, this relation meets the criteria for being a function.

Therefore, this relation **does represent a function**.

**Answer:** This relation represents a function.