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.

Consider the relation that subtracts 11 from a number:

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

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.

The most common way to write this function would be,

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

If we wanted to find out what y is when x is 42, we would substitute 42 for x, and then calculate y.

So we could say that 42 belongs to the domain of the function, and 31 belongs to the range.

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: 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). Given

find f(-2). It’s just a matter of substitution. If you replace every x with –2, Given

It’s just a matter of substitution. If you replace every x with –2, Given you can easily calculate:

It’s just a matter of substitution. If you replace every x with –2, Given you can easily calculate:

Given find: