Functions

What are functions?

A function is a relationship, in which each input has only one output.

The output of a function f  corresponding to an input x is denoted by f (x ) (read "f  of x ")
Example:
For every "x" value there is only one possible "y" value

Something is not a function if one of its "x" values corresponds with two or more "y" values
Example:





Since each "x" value will have a positive and a negative output, it is not a function

How to tell if a relationship is a function using graphing:
A method called "The Vertical Line Test", draws a vertical line through one of the "x" values of the relationship when plotted on a coordinate plane. If the line crosses the graph twice over the same "x" value, then the relation is not a function.

This graph shows a function, because there is no vertical line that will cross this graph twice.

This graph does not show a function, because any number of vertical lines will intersect this oval twice. For instance, the y-axis intersects (crosses) the line twice.

How to tell if a relationship is a function without graphing:

To see if a relationship is a function or not, you can make a T-chart using the "x" and "y" values.

This is a function, because for each value of "x" there is exactly one "y" value.

This is not a function, because the "x" value of 1 corresponds to multiple "y" values (0 and 15).