Functions
What is a function?
 A function consists of:
 A set called the domain containing numbers called inputs,
and a set called the range containing numbers called
outputs.
 The inputs and outputs must be paired such that each input
is paired with one and only one output.
1
2
3
4
0
1
2
3
This input output
table is a function.
1
2
3
4
0
1
2
This input output table is
not a function.
Let’s identify the domain and
range.
 The input-output table shows the cost of various amounts
of regular unleaded gas from the same pump. Identify the
domain and range of the function.
Input
(gallons)
10
12
13
17
Output
(dollars)
19.99
23.99
25.99
33.98
The domain is the set of inputs: 10, 12, 13, 17.
The range is the set of outputs: 19.99, 23.99, 25.99, 33.98.
Let’s try another…
 Identify the domain and range of the function.
Input
0
1
2
4
Output
5
2
2
1
Important Note
 A function may be represented by a mapping diagram.
Notice that an output may be paired with more than one
input, but no input is paired with more than one input.
Input
1
Output
0
2
1
3
2
4
Is this a function?
Output
Input
2
0
3
5
4
20
5
Is this a function?
Input
Output
0
0
1
2
4
8
6
12
Is this a function?
Input
Output
3
1
6
2
9
2
12
1
Is this a function?
Input
Output
2
0
2
1
4
2
7
3
Any Questions?
Lemme Kno’
Holla 
Function Rules
 A function may be represented using a rule that relates
one variable to another.
 The input variable is called the independent variable.
 The output variable is called the dependent variable because
its value depends on the value of the input variable.
 Function rules typically give the dependent in terms of the
independent variable.
 In an equation like y=x+3, you know that y is the dependent
variable.
Writing Functions
 The rule of the function: the output is 3 more than the
input.
 Equation: y=x+3
Input, x
0
1
2
3
4
Output, 3
y
4
5
6
7
Try One…
 The domain of the function y=2x is 0, 2, 5, 7, and 8. Make a
table for the function, then find the range of the function.
x
0
2
5
7
8
y=2x
2(0)=0
2(2)=4
2(5)=10
2(7)=14
2(8)=16
How about this…
 Write the rule for the function.
Input
0
1
4
6
10
Output
2
3
6
8
12
How about a word problem…
 You are buying concert tickets that cost $15 each. You can
buy up to 6 tickets. Write the amount (in dollars) you
spend as the function of the number of tickets you buy.
Identify the independent and dependent variables. Then
identify the domain and range of the function.