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