Graphing Functions Notes

As promised, here they are, the full set of notes for graphing polynomial and rational functions. These notes must be copied by hand into your math dictionaries. Do not hand in the printed pages. There is a good reason for this ... if you really want to know ask me in class. ;-)

Learn Hard!

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Factor and Remainder Theorem Homework

Tonight's homework.

Functions

Function: Functions are set(s) of rules that turn one mathematical object into another.

FUNCTIONS + RELATIONS

-All functions are relations.
-Not all relations are functions.

Four ways of presenting functions: [Using the function f(x) = x + 1]

1) Verbal
...the input changes to an output after adding one unit to it.
2) Graphically: Graph

3) Numerically: Table of Values

4) Symbolically: Equation
f(x) = x + 1

FLAVORS OF FUNCTIONS

1)Many-to-One Function

This is when a function provides one output for two or more inputs.

in the above example; when the input is -2 the output is 3.5, and when the input is 2 the output is 3.5 again.

2) One-to-One Function:

This is a kind function, where there's is only one output for one input.
E.g f(x) = x - 3

FUNCTION COMPOSITION

Function composition dimply means: feeding a function into another.
for e.g.
Note: We can use all the operations on function compositions.

TEST FOR FUNCTIONS:
This is done by the vertical line test, which ensures that there's only one output for each input.
e.g. 1\ Passes 2\ Fails