1. Relations and Functions
Lesson 3-2
Relations and Functions
You'll Learn how to
Identify Functions
Find the domain and range

2. Identify Functions
A function is a special type of relation that pairs an input or
(domain) value with exactly one Output or (range).
Class-Grade relation
Student-age relation
Student
Grade
Student
Age
Bilal
Peter
Selma
Ahmad
Omer 80 85 96
Hamad
Salim
Sally
Rania 12 24 17 31
Each input is paired
with exactly one output
so it’s a function..
an input is paired
with more than one output
so it’s not a function..

3. Ordered pairs Graph Table Mapping Diagram -2 2 3
A relation can be represented in different ways:
Ordered pairs
{(-2, -1), (2, 3), (3, -2)}
Graph
Table
Mapping Diagram x y -2 -1 -1 3 -2 -2 2 3
(2, 3) 2 3 3 -2
(-2, -1)
(3, -2)

4. Reason: there is NO repeated x-value
Find the domain and range
Determine the Domain and the range. Tell whether it’s a function. Explain
From the Table x y
Domain : { 2, 3, 4} 2 3
Range : { 3, 4, 5, 6} 3 4 3
It is NOT a Function 5 4 6
Reason: there is a repeated x-value.
From ordered pairs
{(3, 1), (5, -1), (4, 0), (6, 1)}
Domain : { 3, 5, 4, 6}
Range : { -1, 0, 1}
It is a Function
Reason: there is NO repeated x-value

5. The pencil crosses the graph exactly once. Therefore it’s a Function
Vertical Line Test
The vertical line test is used to determine if a graph is a function.
If a vertical line passes through a graph more than once, then the graph is NOT function.
The pencil crosses the graph exactly once. Therefore it’s a Function

6. The pencil crosses the graph more than once
The pencil crosses the graph more than once. This is not a function because there are two y-values for the same x-value.

7. The pencil crosses the graph more than once
The pencil crosses the graph more than once. This is not a function because there are two y-values for the same x-value.

8. From a graph Domain [-5 , 4] Range [-4 , 3] It is a Function
x y
(4, 3)
Domain
[-5 , 4]
Range
[-4 , 3]
It is a Function
Reason: It passes the vertical line test
(-5, -4)
x y
Domain
[-4 , 3]
Range
[-4 , 4]
It is NOT a Function
Reason: It Does NOT pass the VLT