To determine whether the given set of data points is a function or merely a relation, we need to check if each input [tex]\( x \)[/tex] is paired with exactly one output [tex]\( y \)[/tex]. In other words, an input [tex]\( x \)[/tex] should not map to more than one output [tex]\( y \)[/tex].
Given the data set:
[tex]\[
(-8, 4), (-2, 4), (0, 4), (12, 4)
\][/tex]
We will examine the [tex]\( x \)[/tex]-values to ensure there are no repetitions.
The [tex]\( x \)[/tex]-values from the given points are:
[tex]\[
-8, -2, 0, 12
\][/tex]
Now let's check for duplicates:
1. [tex]\( -8 \)[/tex] appears once.
2. [tex]\( -2 \)[/tex] appears once.
3. [tex]\( 0 \)[/tex] appears once.
4. [tex]\( 12 \)[/tex] appears once.
Since each [tex]\( x \)[/tex]-value occurs only once, each [tex]\( x \)[/tex] maps to exactly one [tex]\( y \)[/tex]-value. This satisfies the definition of a function.
Thus, the given set of data points is indeed an example of a function.
The final answer is:
[tex]\[
\text{Function}
\][/tex]
