Sec 3 Term 3

Functions and Modulus Functions


Passport 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


Fuction_2.jpgFuction_1.gif

c) Definition of : Domain, Range and Image

Domain, Codomain and Range

There are special name for what can go into, and what can come out of a function:
external image yes.gif
What can go into a function is called the Domain
external image yes.gif
What may possibly come out of a function is called the Codomain
external image yes.gif
What actually comes out of a function is called the Range
Let us look at a simple example:
Domain, Range and Codomain
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
2x+3


The Inverse Function just goes the other way:

Inverse
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:
external image function-apple-banana.gif

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:

Function3.jpg
Click on this link to play the absolute game.

f) Solve Equations involving modulus functions

Fuction_4.jpg
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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:
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Passport 4:
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Functions Screenshot
Functions Screenshot