2.1
Relations and Functions
What is a Relation?
• A relation is a set of pairs of inputs and
outputs.
• They can be written as an ordered pair
• They can be graphed
• They can be expressed in a mapping
diagram
Ordered Pairs
{( 0,5), (1,7), (2,6), (5,0)}
• 0, 1, 2, 5 are all
considered “inputs”
• These are all the “x”
coordinates
• 5, 7, 6, 0 are all
considered “outputs”
• These are all the “y”
coordinates
Graph
{( 0,5), (1,7), (2,6), (5,0)}
Mapping Diagram
{( 0,5), (1,7), (2,6), (5,0)}
INPUT
OUTPUT
Create a mapping diagram
{(1,3), (2,9), (5,1), (7,12), (4,2)}
Domain
• Set of all inputs of a relation
• The “x” coordinate
Range
• The set of all outputs of a relation
• The “y” coordinate
Example
Find the domain and range of the relation
Functions
• A function is defined as a relation in which
every input (element in the domain) is
paired with exactly one output (element in
the range).
Mapping diagrams
1
-2
2
1
4
3
5
9
7
12
Every input mapped to exactly one output-this is a function.
Mapping diagrams
1
-2
2
1
4
3
5
9
7
12
7 is mapped to TWO outputs-NOT a function
Graphing
• The vertical line test is used when
determining if a graph of a relation is a
function.
• If we can draw a vertical line through every
part of the graph and have it only go
through ONE point, then the relation is a
function.
Graph
Graph
Ordered Pairs
• When looking at ordered pairs to determine
if they represent a function, there can be no
repeating x’s.
Ordered Pairs-Determine if they
represent a function
{( 0,1), (3,2), (9,1), (7,2)}
{( 0,1), (3,2), (4,9), (0,2)}
Function notation
• When using function notation, we use F(x)
instead of y
How to work with function
notation
For each function, find f(3), f(1) and f(9)
f ( x)  2 x  9
f ( x)  2 x  1
2
Homework
8/29: #6 pg 42 1,2,6-21, 24-37
8/30: #7 pg 534 2-28 even, 36-40 all
8/31: QUIZ 1.3-9.7
9/1: #8 pg 59 2-44 even, 46-48 all, 50-54 even, 56
(use a table to graph)