FunctionsFunctions

What is a function?What is a function?

A A functionfunction consists of: consists of: A set called the A set called the domaindomain containing numbers containing numbers

called inputs, and a set called the called inputs, and a set called the rangerange containing numbers called outputs.containing numbers called outputs.

The inputs and outputs The inputs and outputs mustmust be paired such be paired such that each input is paired with one and only that each input is paired with one and only one output.one output.

1234

0123

1234

01

2

This input output table is a function.

This input output table is not a function.

Let’s identify the domain Let’s identify the domain and range.and range.

The input-output table shows the cost of The input-output table shows the cost of various amounts of regular unleaded gas various amounts of regular unleaded gas from the same pump. Identify the domain from the same pump. Identify the domain and range of the function.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…Let’s try another…

Identify the domain and range of the Identify the domain and range of the function.function.

Input 0 1 2 4

Output 5 2 2 1

Important NoteImportant Note

A function may be represented by a A function may be represented by a mapping diagrammapping diagram. Notice that an output . Notice that an output may be paired with more than one input, may be paired with more than one input, but no input is paired with more than one but no input is paired with more than one input.input.

Input1

2

3

4

Output0

1

2

Is this a function?Is this a function?

Input

0

5

20

Output

2

3

4

5

Is this a function?Is this a function?

Input Output

0 0

1 2

4 8

6 12

Is this a function?Is this a function?

Input Output

3 1

6 2

9 2

12 1

Is this a function?Is this a function?

Input Output

2 0

2 1

4 2

7 3

Any Questions?Any Questions?Lemme Kno’Lemme Kno’

Holla Holla

Function RulesFunction Rules

A function may be represented using a rule that A function may be represented using a rule that relates one variable to another.relates one variable to another. The input variable is called the The input variable is called the independent independent

variablevariable.. The output variable is called the The output variable is called the dependent dependent

variablevariable because its value depends on the value because its value depends on the value of the input variable.of the input variable.

Function rules typically give the dependent in Function rules typically give the dependent in terms of the independent variable.terms of the independent variable. In an equation like y=x+3, you know that y is the In an equation like y=x+3, you know that y is the

dependent variable. dependent variable.

Writing FunctionsWriting Functions

The rule of the function: the output is 3 The rule of the function: the output is 3 more than the input.more than the input. Equation: y=x+3Equation: y=x+3

Input, x

0 1 2 3 4

Output, y

3 4 5 6 7

Try One…Try One…

The domain of the function y=2x is 0, 2, 5, The domain of the function y=2x is 0, 2, 5, 7, and 8. Make a table for the function, then 7, and 8. Make a table for the function, then find the range of the function.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…How about this…

Write the rule for the function.Write the rule for the function.

Input 0 1 4 6 10

Output

2 3 6 8 12

How about a word How about a word problem…problem…

You are buying concert tickets that cost $15 You are buying concert tickets that cost $15 each. You can buy up to 6 tickets. Write the each. You can buy up to 6 tickets. Write the amount (in dollars) you spend as the amount (in dollars) you spend as the function of the number of tickets you buy. function of the number of tickets you buy. Identify the independent and dependent Identify the independent and dependent variables. Then identify the domain and variables. Then identify the domain and range of the function.range of the function.