A function is a special kind of relation.

(A relation is an operation, or series of operations, that maps one number

onto another.)

A function is a special kind of relation.

Functions are the relations that mathematicians study most.

What makes a relation a function?

Good question!

In a function, each input value

can give only one

output value.

Does that make sense?

Then try this:

If you put a number into a function,

you want to know

that only one number can come out.

11x

Consider the relation that subtracts 11 from a number:

11x

If you put a number in, is there only one possible number that could

come out?

11x

23

12

5

16

99

88

Is there any number you can subtract 11 from

and have more than one outcome?For any input value, there is only one possible output value.

So this is a function.

11xy

The most common way to write this function would be,

11xy

When we write it like this, x is always the input value,

and y is always the output value,

11xy

If we wanted to find out what y is when x is 42,

we would substitute 42 for x, and then calculate y.

1142 y 31y

So we could say that 42 belongs to the domain of the function,

and 31 belongs to the range.

11xy

,42When x31y

The domain of a function is the set of all input, or x-, values.

The range of a function is the set of all possible

output, or y-, values.

One common way to write a function uses

function notation.

Function notation looks like this:

12 xxf

Read that, “F of x equals two x plus 1.”

Now it becomes obvious that x is the input variable.

You may be asked questions such as,

find f (-2).

,12 xxf Given

find f(-2).

It’s just a matter of substitution. If you replace every x with –2,

,12 xxf Given

It’s just a matter of substitution. If you replace every x with –2,

Given 2f 1xx2 12

you can easily calculate:

It’s just a matter of substitution. If you replace every x with –2,

Given 2f

you can easily calculate:

14 3

Given

find:

,95 xxf

8f 49 0f 9 7f 26