Introduction To Functions

The Function Machine

A Function In Action

Put a large peperoni pizza into our function machine.


What about an apple?


What will happen when we put a number into the function machine?

Function Terminology

•A function is named with a single letter. We will call our

function machine f.

We can use any letter to designate a function i.e. h, b, t.


Lets call the thing being put into the machine (x).

We would write f (x) = x/2

We say “f of x equals x over 2”

Function TerminologyRelation Vs. Function

Relation- Each number you put in is associated with each number you get out.Function- Every 'input' number is associated with exactly one 'output' number.

All functions are relations. Not all relations are functions.

Function TerminologyThe two definitions seem very similar, but

taking a closer look we will identify the differences.

Can you see the difference?

Relation Function1

3

7

12

3

9

21

64

-2

2

4

22

-4

-3

-2

-1

Function TerminologyDomain

The domain of a function is the set of 'input' numbers for which the function is defined. In the function on the previous slide, the domain is {-2, 2, 4, 22}.Note: The set of input numbers are the values of x. All the values of x make up the domain.

Function TerminologyRange

The range of a function is the set of results to the equation for a given input. A true function only has one result for every domain. In the function on slide 11, the range is {-4, -3, -2, -1}Note: y is the variable associated with range. It can also be expressed as f (x). Also, y or f (x) is considered to be the output values of the function.


• f (x) = x/2• Independent Variable – The variable x

(input) is considered to be the independent variable because its value determines the value of other variables.

• Dependent Variable – The variable y or f (x) (output) is considered to be the dependent variable because it’s value is determined by the value of the variable x.

Function FormsCombining all of our new ideas let’s take a look at

how functions may appear.Using our function from slide 11, we can take the input and output values to form a set of ordered pairs.

The x values (input/domain) are {-2, 2, 4, 22}

The y or f (x) values (output/range) are {-4, -3, -2, -1}

(x,y) =>{(-2,-3),(2, -4),(4, -2),(22, -1)}

Function FormsUsing our function machine f

We found that anything that was put into the machine was cut in half.

We determined that the equation form wasf (x) = x/2

More examples of equation form: g (x) = 3x + 4 t (x) = (-2/3)x – 16

p (x) = 10x

Function Forms

Graphical Representation

• The set of ordered pairs {(0,-4),(1, -2),(2, 0),(3, 2)}

• The equation f (x) = 2x-4

• We can even use this graph to form both the equation and ordered pairs.

This is a graph of a function

We can form this graph given:

Real World Practice

Now It’s your turn . . .Everyone must work together and respect each other at all times.See the handout for more detailed instruction.

Credit• Slide 2,3,4 – Function Machine:

http://www.carlisleschools.org/webpages/wolfer/virtual.cfm

• Slide 3,4 – Pizza: http://www.rivercitypizza.com/

• Slide 5 – Apple: http://fostertech.wordpress.com/2010/07/28/ios-4-iphone-configuration-utility/

• Slide 5 – Half Apple: http://www.istockphoto.com/stock-photo-7523903-red-apple-cut-in-half.php

• Slide 6 – Number 100: http://www.minnesotafirsthome.com/buyers/100-financing-mn-first-time-buyers-only/

• Slide 6 – Number 50: http://www.radiowaves.co.uk/r/barto99

• Slide 16 – Graph: http://www.algebra.com/algebra/lessons/graphing/linear.epl

Introduction To Functions

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Transcript of Introduction To Functions