Relations And Functions Math 10C

Front 1

Set

Back 1

A collection of objects. Example a set of even numbers. {2,4,6,8...}

Front 2

Element

Back 2

Objects in a set

Front 3

Relation

Back 3

Associates the elements of one set with the elements of another set. Example Comparing coin names with their values:

{(pennies,0.01),(nickels,0.05),(dimes,0.10),...}

Front 4

How to describe a relation

Back 4

1. In words (by writing how they are associated)

2. As a set of ordered pairs. {(0,6),(1,12)}

3. As a mapping diagram/arrow diagram

4. As a table

5. As a graph(if we have numbers in one of the sets)( ex. Bar, line, etc)

Front 5

Function

Back 5

A special type of relation

Where each element in the domain is associated with exactly one element range

For every input there is only one output

Front 6

Domain

Back 6

All the elements in the first set

(Independent)

Front 7

Range

Back 7

All the elements in the second set (dependent)

Front 8

Functional Notation

Back 8

Notation used to show the independent variable

y=replace f(x)-read f of x- the function depends on x

The out put depends on the input

1 in algebra, symbols such as x and y are used to represent numbers

2. To represent functions we use symbols such as f(x) and g(x) instead of y

Front 9

Write y=2x+5 in functional notation

Back 9

f(x)=2x+5

Front 10

VLT

Back 10

Vertical line test

If we are given the graph of a relation, we can determine whether it is a function by using the Vertical Line Test

If two points on a graph can be joined by a vertical line, then it is not a function

When x repeats itself= not a function

Front 11

Domain and Range

Back 11

Domain and range describes the location of the graph. It does NOT tell you the shape or rate of change in values

Domain is x values

Range is y values