How do you know if a relation is a function?

1 answer

The most important property is that it should satisfy the vertical line test.

This means that if it is possible to draw a vertical line through some point on the graph of the relation such that it intersects the graph at more than one point, it is NOT a function.

Mathematically, it means that every element in the domain is mapped by the relation to one single value in the range.

Example of relations that are not functions:
y=&sqrt(x)
y=arcsin(x)

Examples of functions:
y=x
y=x²
all polynomials
y=sin(x)
y=ex