To determine whether the given set of ordered pairs represents a function, we need to evaluate whether each unique \( x \)-value corresponds to exactly one unique \( y \)-value. In other words, an \( x \)-value should not map to multiple \( y \)-values for the set to be a function.
Given the set of ordered pairs:
[tex]\[ \{(-5, -5), (-1, -2), (0, -2), (3, 7), (8, 9)\} \][/tex]
Let's examine the \( x \)-values and their corresponding \( y \)-values:
1. For \( x = -5 \), \( y = -5 \)
2. For \( x = -1 \), \( y = -2 \)
3. For \( x = 0 \), \( y = -2 \)
4. For \( x = 3 \), \( y = 7 \)
5. For \( x = 8 \), \( y = 9 \)
We observe the following:
- Each \( x \)-value in the set is unique.
- No \( x \)-value is repeated with a different \( y \)-value.
Since every \( x \)-value in the set corresponds to exactly one \( y \)-value, this set of ordered pairs represents a function.
Hence, the answer is:
C. Yes, because every [tex]\( x \)[/tex]-value corresponds to exactly one [tex]\( y \)[/tex]-value.
