Download Presentation
Functions 3.5

Loading in 2 Seconds...

1 / 56

# Functions 3.5 - PowerPoint PPT Presentation

Functions 3.5. An Introduction to Funtions. Independent and Dependent Variables. Independent and Dependent Variables. Definitions Indepdent Variable: the variable that someone/something changes directly Dependent Variable: the result of the independent variable changing.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about 'Functions 3.5' - tyler

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Functions 3.5

An Introduction to Funtions

Independent and Dependent Variables

Definitions

Indepdent Variable: the variable that someone/something changes directly

Dependent Variable: the result of the independent variable changing

Independent and Dependent Variables

independent(cause) dependent(effect)

Examples:

ind: hours I study for class

dep: grade in class

Independent and Dependent Variables

ind: hours I worked in a pay period

dep: how much I got paid

Independent and Dependent Variables

ind: amount of time spent on the treadmill this week

dep: blood pressure

Independent and Dependent Variables

There is a relationship between the independent and dependent variable

This relationship can be shown using an ordered pair

(x,y)

(cause, effect)

Functions

Function: a relation in which, for each value of the first component there is exactly one value of the second component

Example: Remote control

(x,y)

(cause, effect)

Functions

You can create your own function

F={(1,1), (2,2),(3,3),(4,4)}

This is a function because . . . ?

Functions

Function or Not a Function

Is H a function? Why or Why not?

H={(4,12),(3,7),(5,23)}

Functions

Function or Not a Function

Is H a function? Why or Why not?

H={(4,12),(3,7),(5,23)}

Functions

Function or Not a Function

Is G a funtion?

G={(1,1),(2,5),(3,7),(4,1)}

Functions

Function or Not a Function

Is G a funtion?

G={(1,1),(2,5),(3,7),(4,1)}

Look closely at G

You can have the same out put for different inputs

Just as on your computer you can have two buttons(input) do the same action(output)

Example: (Shift Key)

Real World Functions

Assume You own a resturant

You require the host to always say "Welcome. How many will be in your party today?", every time someone walks through the door.

This is a function (input, output)

H = ([Person enters door], [Greeting])

Greeting customersdepends on people walking through the front door.

Only greet customers when someone enters!!!

Real World Functions

Usher at the movie

When ever a movie end, clean the theater

U = (Movie Ends, Clean Theater)

cleaning of the theaterdepends on the moving ending.

Only clean the theater when the movie ends!

Real World Functions

Any other examples of functions?

Functions

Function only if for every input there is one output

D = {(2,5), (3,4), (1,8) (2,7), (4,5)}

Why is this not a function?

Think back to remote control.

Functions

Function only if for every input there is one output

D = {(2,5), (3,4), (1,8) (2,7), (4,5)}

Why is this not a function?

Think back to remote control.

Functions

Function of Not a Function?

{(1,2),(3,4),(5,6)}

Function or Not a Function

Why?

Functions

Function of Not a Function?

{(1,2),(3,4),(5,6)}

Function or Not a Function

Why?

Functions

Function of Not a Function

{(1,2), (2,2), (3,2), (4,2), (5,2) }

Why?

Functions

Function of Not a Function

{(1,2), (2,2), (3,2), (4,2), (5,2) }

Why?

Function

Functions

Function of Not a Function

{(1,2), (2,2), (3,2), (4,7), (3,8) }

Why?

Functions

Function of Not a Function

{(1,2), (2,2), (3,2), (4,7), (3,8) }

Why?

Not a Function

Functions

Function of Not a Function

{(2,4), (6,8), (10,12), (14,16), (18,20) }

Why?

Functions

Function of Not a Function

{(2,4), (6,8), (10,12), (14,16), (6,20) }

Why?

Not a Function

Functions

Function of Not a Function

{(1,4), (2,8), (12,12), (7,4), (8,8) }

Why?

Functions

Function of Not a Function

{(1,4), (2,8), (12,12), (7,4), (8,8) }

Why?

Function

Domain and Range

The domain is set of all values of the independent variable(x)

The range is the set of all values of the dependent variable(y)

Domain and Range

Example

{(1,2),(3,4),(5,6),(7,8)}

Domain is{1,3,5,7} First Component of the ordered pair

Range is {2,4,6,8} Second Component of the ordered pair

Domain and Range

What is the Domain and Range?

{(1,7), (10,16), (4,-2)}

Domain?

Range?

Domain and Range

What is the Domain and Range?

{(1,7), (10,16), (4,-2)}

Domain {1, 4, 10}

Range {-2, 7, 16, }

Domain and Range

What is the Domain and Range?

{(-5, 31), (6,-1), (-7,-18)}

Domain?

Range?

Domain and Range

What is the Domain and Range?

{(-5, 31), (6,-1), (-7,-18)}

Domain {-7, -5, 6}

Range {-18 ,-1 31}

Domain and Range

What is the Domain and Range?

{(0 -3), (4,-3), (-4,0)}

Domain?

Range?

Domain and Range

What is the Domain and Range?

{(0 -3), (4,-3), (-4,0)}

Domain {-4, 0, 4}

Range {-3,0}

Domain and Range

What is the Domain and Range?

{(1, 2), (2,2), (3,2)}

Domain?

Range?

Domain and Range

What is the Domain and Range?

{(1, 2), (2,2), (3,2)}

Domain {1, 2, 3}

Range {3}

Finding Domains and Ranges From a Graph

What is the domain and range?

Domain {-1, 1, 2 }

Range {-1, 1, 2}

Finding Domains and Ranges From a Graph

Try on your own.

What is the domain and range

Domain

Range

Finding Domains and Ranges From a Graph

• Try on your own.
• What is the domain and range
• Domain {-4, -2, 3}
• Range {-2, -1, 1}
Finding Domains and Ranges From a Graph

What is the domain and Range of this graph?

Domain?

Range?

Finding Domains and Ranges From a Graph

• Try on your own
• What is the domain and Range of this graph?
• Domain [-2, 2]
• Range [-1, 4]
Finding Domains and Ranges From a Graph

Try on your own

What is the domain and Range of this graph?

Domain?

Range?

Finding Domains and Ranges From a Graph

What is the domain and range for this graph

Arrow heads mean continue indefinitely

Domain(-∞, ∞)

Range (-∞, ∞)

Finding Domains and Ranges From a Graph

Try This One

What is the domain and range for this graph?

Arrow heads mean continue indefinitely

Domain(-∞, ∞)

Range (-∞, ∞)

Finding Domains and Ranges From a Graph

What is the domain and range for this graph?

Arrow heads mean continue indefinitely

Domain(-∞, ∞)

Range [-1, ∞)

Finding Domains and Ranges From a Graph

Try this One

What is the domain and range for this graph?

Arrow heads mean continue indefinitely

Domain(-∞, ∞)

Range (- ∞, 4]

Vertical Line Test

The vertical line test determines if a graph is a function

Use: draw a vertical line anywhere on the graph.

If it crosses the graph more than once it is not a function

Vertical Line Test

• Any vertical line drawn here will only cross once.
• There fore it passes the vertical line test
Vertical line test

Does This Pass the vertical line test

Function or Not

Vertical Line Test
• This does not pass the vertical line test
• Most lines would cross this graph more than once