FUNCTIONSClassifying Relationships

Functions The definition of a function is:

A function is a relation that maps each element in the domain to one and only one element in the range.

What??? What is domain?

Domain is the “x” values. What is range?

Range is the “y” values. So a function in plain English is:

A relation where “x” is not repeated.

Functions

There are different ways to determine if a relation is a function depending on how the relation is presented.

If you have a list of points, look to see if “x” is repeated. {(1, 2), (4, 6), (5, 5), (-2, -1)}

Function – nothing repeats {(-2, -2), (5, -2). (4, 6), (-5, -2)}

Function – it is still a function if “y” repeats {(-1, 2), (4, 4), (6, 5), (4, 8)}

Not a function – 4 is repeated

Functions When information is presented as a map,

look at the arrows. Multiple arrows from the first column mean not a function.

This is a function because each time has its own event.

Start Time1 pm3 pm5 pm7 pm

Athletic Event

FootballVolleyball

SoccerBasketball

Functions

This is not a function because 7 pm is used twice.

Start Times1 pm3 pm7 pm

Functions

When you are give a picture, use the vertical line test.

To do the vertical line test, draw a vertical line on the picture.

If it crosses more than once, it is not a function.

Not a function

Function

Not a function

Not a Function

Function

Functions

Other relations are given as equations. Think about what graph the equation will

create. y = 2x + 1 Line y = x2 + 3x -7 Parabola y = |x - 7| Absolute Value (“v” shape) y = Square Root (half of a parabola) (x -1)2 + (y -4)2 = 16 Circle

If it is “x = “, it is never a function.