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Functions
TEXTBOOK REFERENCE:
4-6
What is a relation?
A relation is any set of
ordered pairs.


{(3,4), (4,5), (5,6)}

{(3,4), (3,5), (3,6)}
Each number in the set of
ordered pairs is called an element.

All ordered pairs
are relations!
What is a function?
 A function is a relation in which
only one x matches with a y
All x coordinates are different
numbers = function!




Relation and Function
{(3,4), (4,5), (5,6)}
Relation only
{(3,4), (3,5), (4,6)}
Functions as Ordered Pairs
{(4,5), (-1, 0), (3,0)}
All x are different, y
does not matter!

Functions as Tables
{(4,5), (-1, 0), (3,0)}
x
y
-1
0
3
3
4
5
Functions as Graphs
Which of the graphs
below represents a
function?
A graph that is a function must
pass the vertical line test
Place your pencil vertically on
the graph! If your pencil
touches the picture only once,
you have a function!
Function
Function Parts
A function is a relationship
where on thing depends
upon another.
A function has three parts:
Input – x (plug in number)
Function Rule– problem
(arithmetic or geometric sequence)
Output – y (answer)
Making Function Tables
A function table organizes your work
so you can find out what the ordered
pairs are.
Input Function
Rule
x
5x
1
5x1
2
5x2
3
5x3
4
5x4
Output Ordered
Pairs*
y
(x, y)
5
(1, 5)
10
(2, 10)
15
(3, 15)
20
(4, 20)
Making Function Graphs
A function graphs plots the ordered pairs you
found on the coordinate plane
Input
1
2
3
4
x
Function
Rule
2x
2x1
2x2
2x3
2x4
Output
2
4
6
8
y
Ordered
Pairs*
(x, y)
(1, 2)
(2, 4)
(3, 6)
(4, 8)
Real World Function Graphs
Chuck earns $4 an hour cleaning his room. Create
table and graph to represent this situation.
Input
Function
Rule
X
4x
hours
$4 x hours
1
4 x 1 hour
2
4 x 2 hours
3
4 x 3 hours
4
4 x 4 hours
Output
Y
Pay $
$4
$8
$12
$16
Ordered
Pairs*
(x, y)
(1, 4)
(2, 8)
(3, 12)
(4, 16)
What are Linear Equations?
A linear equation is an
equation that forms a
a straight line when
graphed.
y = 2x + 1
y is output although listed
first.
X = the input.
Steps for Graphing Linear Equations
1. Create a four-column
2.
3.
4.
5.
6.
function table.
Select any four values
or numbers to
substitute for the input
x (I suggest -1, 0, 1, 2)
Perform rule.
Write output.
List ordered pairs.
Graph on Coordinate
Plane.
Steps for Graphing Linear Equations, cont’d.
x
2x+1
y
(x, y)
2
2(2)+1
5
(2, 5)
1
2(1)+1
3
(1, 3)
0
2(0)+1
1
(0, 1)
-1
2(-1)+1
-1
(-1, -1)
Steps for Graphing Linear Equations, cont’d.
Every point on the line is a
solution to y =2x +1.