Question

Do the ordered pairs below represent a relation, a function, both a relation and a function, or neither a relation nor a function?
(-4,0) , (2,-6) , (4,-8) , (10,-14) A. Relation only
B. Neither a relation nor a function
C. Function only
D. Both a relation and a function

Answer 1

Answer: D) Both a relation and a function

=======================================================

Explanation:

A relation is any set of (x,y) points usually with some rule tying them together. Though that rule doesn't have to be present. We could simply have a set of points. The set of points we are given is a relation.

A function occurs when we don't repeat the x value. Visually if we had two points stacked on top of each other, then we wouldn't have a function since it fails the vertical line test. A function happens when all x inputs leads to exactly one y output. If we had say { (-4,0), (2,-6), (-4,3) } then this wouldn't be a function since x = -4 repeats itself.

Since none of the x values repeat themselves in our given set, this means we have a function.

Side note: Any function is a relation, but not the other way around.