Basic Algebra/Lines (Linear Functions)/Functions and Relations

Lesson

y = x^2

Is this a function?

versus, y^2 = x

Is this a function?

The first equation is a function because x has only one y-value, whereas the second equation has many values.

In a function, each domain value or x-value should only have one y-value, otherwise it is not a function.

Definition: In two sets, A and B, a function is a mapping from A to B.

This mapping should satisfy the following conditions in order for it to be a function:

1. All the elements of set A should be paired with any element of set B.
2. An element of set A should not be paired with more than one element of set B. (i.e. the first coordinates of an ordered pairs should not be repeated)