FUNCTIONS

WHAT IS A FUNCTION?

• A function is a relationship between inputs and outputs.
• Each input leads to exactly one output.
• In a function, X never repeats and only has one Y.
• You can tell if it's a function by using the vertical line test.

WHAT'S A VERTICAL LINE TEST?

• A vertical line test is a test to see if there's a function or not.
• You use vertical lines on a graph and see if more than one point is on it.
• If only one point is on each vertical line, it's a function.
• If more than one point is on each line, then it is not a function.
• It is very simple and easy to do. It is also very efficient as well.

EXAMPLE

• This is what a function would look like:
• {(4,1), (5,2), (6,6), (1,9), (3,4)}
• This would be an ordered pair.
• An ordered pair is one representation of functions.

DIFFERENT REPRESENTATIONS

• This is a table representation of this function:

DIFFERENT REPRESENTATIONS

• You can also use graphs to represent functions:

DIFFERENT REPRESENTATIONS

• Another way to represent functions is by mapping them:

DIFFERENT REPRESENTATIONS

• Here's an equation representation of the function:
• 4=1
• 5=2
• 6=6
• 1=9

WHAT IS A NON-FUNCTION?

• A non-function is the opposite of a function.
• How can you tell if it's a non-function?
• If X repeats itself, it is a non-function.
• If X has more than one Y, it is a non-function.
• If it fails the vertical line test, it's a non-function.

EXAMPLE

• This is an example of a non-function:
• {(1,2), (2,3), (2,4), (4,5), (1,6)}
• These are ordered pairs.

DIFFERENT REPRESENTATIONS

• Here's a table representation of a non-function:

DIFFERENT REPRESENTATIONS

• This is a graph representation of a non-function:

DIFFERENT REPRESENTATIONS

• Now here's a non-function in mapping:

DIFFERENT REPRESENTATIONS

• This is an equation representation of a non-function:
• 1=2
• 2=3
• 2=4
• 4=5

THAT'S IT FOR FUNCTIONS!