To determine which relation is also a function, we need to recall the definition of a function. A relation is a function if every element of the domain (the set of all possible x-values) is mapped to exactly one element of the range (the set of all possible y-values).
Option A:
[tex]\[
\{(-8,8),(-6,5),(-6,4),(-3,1),(-1,0)\}
\][/tex]
- Here, -8 is mapped to 8.
- -6 is mapped to 5.
- -6 is also mapped to 4.
- -3 is mapped to 1.
- -1 is mapped to 0.
In this set, the value -6 from the domain corresponds to two different values in the range, which are 5 and 4. According to the definition of a function, -6 should only map to one value. Therefore, this relation is not a function.
Option B:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
10 & 1 \\
\hline
15 & 2 \\
\hline
15 & 3 \\
\hline
\end{array}
\][/tex]
- Here, 10 is mapped to 1.
- 15 is mapped to 2.
- 15 is also mapped to 3.
In this table, the value 15 from the domain corresponds to two different values in the range, which are 2 and 3. According to the definition of a function, 15 should only map to one value. Therefore, this relation is not a function.
Based on the analysis, none of the given choices (Option A and Option B) represent a relation that is also a function.
