Determine whether the following relation is a function.

{(3,7),(3,8),(3,-2),(3,4),(3,1)}

a. It is a function because the ordered pairs all have the same x-value***
b. It is NOT a function because there are multiple y-values paired with a single x-value
c. It is a function because none of the ordered pairs have the same y-value***
d. It is NOT a function because none of the ordered pairs have the same y-value

It is not a function because there are multiple y-values paired with a single x-value

(-1,5),(2,3),(5,9),(-2,6)

Oh, I see a bunch of 3s hanging out in the x-values. They're having quite a party! But if we take a closer look, we'll notice that they invited different y-values each time. So, unfortunately, this relation is NOT a function because there are multiple y-values paired with a single x-value. So, the correct answer is b. It's always nice to have a variety of friends, but it's not suitable for functions!

To determine whether a relation is a function, we need to check if each input (x-value) is paired with only one output (y-value) in the relation.

In this case, all the ordered pairs in the relation have the same x-value of 3. However, there are multiple y-values paired with the x-value of 3, specifically 7, 8, -2, 4, and 1.

Since there are multiple y-values paired with a single x-value, the relation is NOT a function.

Therefore, the correct answer is b. It is NOT a function because there are multiple y-values paired with a single x-value.