There are special name for what can go into, and what can come out of a function:

What can go into a function is called the Domain

What may possibly come out of a function is called the Codomain

What actually comes out of a function is called the Range

Let us look at a simple example:

Domain, Range and Codomain

In this illustration:

the set "A" is the Domain,

the set "B" is the Codomain,

and the set of elements that get pointed to in B (the actual values produced by the function) are the Range, also called the Image.

In that example:

Domain: {1, 2, 3, 4}

Codomain: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Range: {3, 5, 7, 9}

d) Inverse Function

An inverse function goes in the opposite direction!
Let us start with an example:

Here we have the function f(x) = 2x+3, written as a flow diagram:

2x+3

The Inverse Function just goes the other way:

Inverse

So the inverse of: 2x+3 is: (y-3)/2

Back to Where We Started

The cool thing about the inverse is that it should give you back the original value:

If the function f turns the apple into a banana,then the inverse function f-1 turns the banana back to the apple

So applying a function f and then its inverse f-1 gives us the original value back again: f-1( f(x) ) = x
We could also have put the functions in the other order and it still works: f( f-1(x) ) = x e) Modulus Function
The modulus of a number is the magnitude of that number. For example, the modulus of -1 ( |-1| ) is 1. The modulus of x, |x|, is x for values of x which are positive and -x for values of x which are negative. So the graph of y = |x| is y = x for all positive values of x and y = -x for all negative values of x:

Passport 2: Click on this link to download the notes for this unit and complete all the worked examples. If you can handle the worked examples here you should be attaining 85% enlightenment.

Passport 3: Click on this link and download the assignment and complete it. Upload your solution into IVLE under student submssion function. Save your file as : EthanKoh3O211FunctionAss1

Passport 4: Click on this link and play this game to ensure that you have attain full enlighten of this unit.

Sec 3 Term 3Functions and Modulus FunctionsPassport 1:## a) Definition of Function

## Reading 1:http://archives.math.utk.edu/visual.calculus/0/functions.11/index.html

## b) Introduction to function

## Reading 1:http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut30_function.htm

## c) Illustrate a relation using arrow diagram

## c) Definition of : Domain, Range and Image

## Domain, Codomain and Range

There are special name forwhat can go into, andwhat can come outof a function:intoa function is called theDomainmay possibly come outof a function is called theCodomainactually comes outof a function is called theRange## d) Inverse Function

An inverse function goes in the opposite direction!Let us start with an example:

f(x) = 2x+3, written as a flow diagram:## Back to Where We Started

The cool thing about the inverse is that it should give you back the original value:If the function f turns the apple into a banana,then the

inversefunction f-1 turns the banana back to the appleSo applying a function f and then its inverse f-1 gives us the original value back again:

f-1( f(x) ) = x

We could also have put the functions in the other order and it still works:

f( f-1(x) ) = x

e) Modulus FunctionThe modulus of a number is the magnitude of that number. For example, the modulus of -1 ( |-1| ) is 1. The modulus of x, |x|, is x for values of x which are positive and -x for values of x which are negative. So the graph of y = |x| is y = x for all positive values of x and y = -x for all negative values of x:

Click on this link to play the absolute game.

## f) Solve Equations involving modulus functions

Watch these videos.

Passport 2:Click on this link to download the notes for this unit and complete all the worked examples. If you can handle the worked examples here you should be attaining 85% enlightenment.

Passport 3:Click on this link and download the assignment and complete it. Upload your solution into IVLE under student submssion function. Save your file as : EthanKoh3O211FunctionAss1

Passport 4:Click on this link and play this game to ensure that you have attain full enlighten of this unit.