Which relations are functions?
{(2, 4), (–1, 7), (3, 0), (5, 4)}
{(–4, 0), (–4, 8), (–1, 3), (2, 9)}
{(–6, 1), (0, 1), (2, 1), (3, 1)}
{(–3, –3), (–1, 6), (4, 5), (5, 4)}

Question

Which relations are functions?
         {(2, 4), (–1, 7), (3, 0), (5, 4)} 
        {(–4, 0), (–4, 8), (–1, 3), (2, 9)} 
        {(–6, 1), (0, 1), (2, 1), (3, 1)} 
        {(–3, –3), (–1, 6), (4, 5), (5, 4)}

solomonzelman · Answer

A function is not allowed to have more than one output (y-value) for a single input (x-value).
If you see 2 points with the same y-coordinate in 1 relation, then this relation is not a function.

solomonzelman · Answer

If all the points in a relation have DIFFERENT y-values, then, even if any of the points (and even if all of them) have the same x-values, then the relation is (still) a function.
(as long the y-coordinate doesn't repeat more than once)

solomonzelman · Answer

yes, 2 is a function, because all outputs (y-values) are different.

solomonzelman · Answer

yes.

solomonzelman · Answer

Yes, and for number 3 it is just a vertical line (not a function, and slope is undefined)
And 1 is not a function either, because 1st and last point in this (the 1st) relation repeat.

solomonzelman · Answer

Glad to help you. You are quick to understand:) You welcome...