Question

State the domain and range of the relation. Determine whether the relation represents a function.
StartSet left parenthesis negative 15 comma negative 15 right parenthesis comma left parenthesis 0 comma 0 right parenthesis comma left parenthesis 15 comma 15 right parenthesis EndSet

Answer 1

To determine the domain and range of the given relation, we first identify the sets of ordered pairs:

Set: \(\{ (-15, -15), (0, 0), (15, 15) \}\)

### Domain:
The domain of a relation is the set of all first elements (x-coordinates) of the ordered pairs.

From the given pairs:
- The first element of \((-15, -15)\) is \(-15\).
- The first element of \((0, 0)\) is \(0\).
- The first element of \((15, 15)\) is \(15\).

Thus, the domain is:
\[
\text{Domain} = \{-15, 0, 15\}
\]

### Range:
The range of a relation is the set of all second elements (y-coordinates) of the ordered pairs.

From the given pairs:
- The second element of \((-15, -15)\) is \(-15\).
- The second element of \((0, 0)\) is \(0\).
- The second element of \((15, 15)\) is \(15\).

Thus, the range is:
\[
\text{Range} = \{-15, 0, 15\}
\]

### Function Determination:
A relation is considered a function if each element in the domain corresponds to exactly one element in the range (i.e., no x-coordinate is repeated with a different y-coordinate).

In this case, each x-coordinate \(-15\), \(0\), and \(15\) maps to a unique y-coordinate \(-15\), \(0\), and \(15\), respectively. There are no repeated x-coordinates associated with different y-coordinates.

Therefore, the relation does represent a function.

### Summary:
- **Domain:** \(\{-15, 0, 15\}\)
- **Range:** \(\{-15, 0, 15\}\)
- **Represents a function?** Yes.