Determine whether the relation is a function. [(-4,6),(-1,3),(3,3),(8,-9)]

Function:

for every element in the domain (the x's) there is one and only one value in the range (the y's)
or in simpler terms
We do not want to see two or more different points with the same x value.

so what do you think?

To determine whether the relation is a function, we need to check if each input (x-value) has a unique output (y-value).

One way to do this is to look for any repeating x-values. In the given relation, the x-value -1 appears only once, and its corresponding y-value is 3. Therefore, we can conclude that (-1,3) is a valid pair.

Next, we check the x-value 3. It appears twice in the relation, but both times it is paired with the same y-value, which is 3. This means that for x = 3, there is only one corresponding y-value, so we can say that (3,3) is also a valid pair.

Lastly, we look at the remaining x-values: -4 and 8. Both of these values appear only once in the relation, so we can conclude that (-4,6) and (8,-9) are also valid pairs.

Since each x-value is associated with a unique y-value, we can determine that the relation is a function.