Functions
Chapter 4
What makes a graph a
function?

The graph passes the vertical line test
Passes
Fails
What makes a graph a
function?
Each domain (x-value) is
mapped to only one range (yvalue).
 We create a “mapping” to see if
a relation (set of ordered
pairs) is a function.

Domain & Range

Domain: all x-values


List in braces from least to greatest and do
not repeat values
Range: all y-values

List in braces from least to greatest and do
not repeat values
Domain & Range Example
{(3, 4), (-2, 7), (9, 10), (9, 11)}
Domain {-2, 3, 9}
Range {4, 7, 10, 11}
Mapping Diagram
FUNCTION:
(4, 5), (-2, 7), (3, 7), (0, -1)
-2
0
3
NOT A FUNCTION:
(4, 5), (4, -3), (-1, 2), (6,0)
-1
-1
-3
5
7
4
6
0
2
5
4
Try using the vertical line test…does the relation pass?
Make a Table, Mapping, &
Graph
{(9, 2), (-3, 4), (1, 5), (-1, 2)}
Table
Mapping
Graph
Types of Functions
Linear
 Quadratic
 Absolute Value
 Exponential
 Cubic

Let’s GRAPH!

Create a T-Chart
x
y
Graphing Continued:






Pick values for x.
Plug in x and use PEMDAS to solve for y.
Plot ordered pairs.
Connect the points.
Include arrows at the end of your line.
CHECK your work 
Try these linear functions:
1.
2.
3.
y = 3x + 1
y = -2x + 3
1
y= 2x–4
What patterns do you see between the
equations and the graph?
Functions
Chapter 4
What makes a graph a
function?

The graph passes the vertical line test
Passes
Fails
What makes a graph a
function?
Each ____________________ is
mapped to only one ___________
______________.
 We create a “________________”
to see if a ________________
(set of ordered pairs) is a
________.

Domain & Range

Domain: all x-values


List in braces from least to
greatest and do not repeat values
Range: all y-values

List in braces from least to
greatest and do not repeat values
Domain & Range Example
{(3, 4), (-2, 7), (9, 10), (9, 11)}
Domain ____________________
Range _____________________
Mapping Diagram
FUNCTION:
(4, 5), (-2, 7), (3, 7), (0, -1)
NOT A FUNCTION:
(4, 5), (4, -3), (-1, 2), (6,0)
Try using the vertical line test…does the relation pass?
Make a Table, Mapping, &
Graph
{(9, 2), (-3, 4), (1, 5), (-1, 2)}
Table
Mapping
Graph
Types of Functions
Linear
 Quadratic
 Absolute Value
 Exponential
 Cubic

Let’s GRAPH!

Create a T-Chart
Graphing Continued:






Pick values for _____.
Plug in x and use _______ to solve for __.
Plot ordered ______.
Connect the _________.
Include ________ at the end of your line.
_________ your work 
Try these linear functions:
1.
2.
3.
y = 3x + 1
y = -2x + 3
1
y= 2x–4
What patterns do you see between the
equations and the graph?