A function is a mathematical expression which changes one number into another..
It always changes a number the same way.

Let's look at an example of a function. We won't tell you what the function is doing, but you can experiment with different numbers, to try to find out what changes the function is making to your number.

Access the 'Mystery Function'  here

Here are some more examples of some simple functions:

'Double It'
This function doubles a number.
For example, it changes  5  into  10.

'Triple and Add One'
This function multiplies a number by three, and then adds 1.
For example, it changes  5  into  16.

'Remove the Negative'
This function turns negative numbers into positive ones.
For example, it changes  -5  into  5.
It doesn't do anything to positive numbers.

Functions can be described in mathematical terms, to make them easier to write.
The number you want to change is usually represented by   x

Here are the same three examples from above, written in mathematical notation:

This function doubles a number.
For example, if  x  is  5, the result is  2 x 5 = 10.

3x + 1
This function triples a number and adds 1.
For example, if  x  is  5, the result is  3 x 5 + 1 = 16.

This function makes a negative number become positive.
For example, if  x  is  -5, the result is  |-5|  =  5.

There are obviously many different functions. If you need to refer to several different functions in the same question, it is often useful to label each function with a lower-case letter of the alphabet.
Conventionally, the lettering begins with  f (for 'function'), and works upwards through the alphabet.
Let's use this method to label our three example functions above. We'll use  f,  g,  and h.

f = 2x           g = 3x + 1           h = |x|

Finally, the function label will also include the variable which you will be filling in.
In all our examples, this has always been  x. Nevertheless, labelling a function requires you to specify what the variable is.
So our three function examples would be labelled this way:

f(x) = 2x           g(x) = 3x + 1           h(x) = |x|

This is called function notation. On  page two, we'll show you how function notation is used, and why it makes writing questions much simpler. Sr. High students may first want to learn what functions look like  graphically.

Functions Graphically  |  Function Notation

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