what is a function

HousekeepingLast week: • Unit 1 Pretest – Functions• MAP tests

Unit 1 FunctionsUnit Summary: In this unit, students will be introduced to the concept of functions. Emphasis will be placed on the definition of function, domain and range, evaluating functions, calculating slope of a linear function, identifying the rate of change of a function and whether it is increasing or decreasing, and representing functions in different ways.

Learning Objectives: Upon successful completion of this unit, students will be able to:• define function• recognize a function and determine its domain and range• evaluate a function using substitution• calculate slope and compare rates of change for linear

functions• construct an equation from a graph or table of values• model real world situations with functions

Essential Questions/What is the Purpose for Learning This?

Make sure you can answer these questions before attempting the Unit Test.

Why are relations and functions represented in multiple ways?

How are properties of functions and functional operations useful?

Lesson ContentLesson 1: Defining Functions--learn the definition of a function; determine the domain and range; recognize when an equation is not a functionLesson 2: Evaluating Functions--use substitution to evaluate a function; realize that for a function, every input has only one outputLesson 3: Comparing Functions--calculate slope; compare the rate of change for various equations; represent functions in multiple waysLesson 4: Using Functions to Model Linear Relationships--interpret the rate of change from a model; identify if a function is increasing or decreasing; construct and equation with information from a graph or table

Lesson 1: Defining a Function

• learn the definition of a function• determine the domain and range• recognize when an equation is not a function

Why are functions important to me if I’m buying candy at the local store?

In this lesson you will learn what a function is by

evaluating examples of relations.

A relation is any pairing of numbers.

Candy Bars to Price

Paul: (2 bars, $1.50)You: (2 bars, $3.50)

Candy Palace

(2 bars, $1.50)(2 bars, $3.50)(3 bars, $5.00)

Sweet Factory

(1 bars, $0.75)(2 bars, $1.50)(3 bars, $2.25)

Two Kinds of Relations

No RuleRule

A FUNCTION is a special type of relation in which a rule assigns every input exactly one

output.

4321

Inputs

12963

Outputs

Function

A Common MistakeInput (x) Output (y) Output (y)Input (x)

1 2 3 4

3 6 9 12

1 2 3 4

3 6 9 12Function! Not a function!

A FUNCTION is a special type of relation in which a rule assigns every input exactly one

output.

Bars Price

1 $0.75

2 $1.50

3 $2.25

4 $3.00Function

Candy Bars to Price

Paul: (2 bars, $1.50)You: (2 bars, $3.50)

Not a

Function

Weeks Books

1 2

2 4

3 6

4 8

… …

Reading Two Books / Week

Is the Relation a Function???

Hours Problems Correct1 341 652 422 323 534 67

Multiplication Facts

MayCoryBarb

SusanSilasLisa

If I tell you the input, can you

predict the output?

Is the Relation a Function???

Input Output

1 3

2 6

3 9

4 12

Input Output

1 1

2 4

3 9

4 16

Input times 3 Input squared

Is the Relation a Function???

How do you figure out if a gumball machine models a

function relation?

Gumball Machine ExampleInput (x) Output (y)

Gumball Machine ExampleInput (x) Output (y)

123

246

Gumball Machine ExampleInput (x) Output (y)

123

462

Another Gumball Machine Example

Input (x) Output (y)

Another Gumball Machine ExampleInput (x) Output (y)

112

234

Another Gumball Machine ExampleInput (x) Output (y)

1

2

234

A FUNCTION is a special type of relation in which a rule assigns every input exactly one output.