Algebra 1Unit 4

GRAPHING STORIES:

Watch the videos on the next two slides and graph the story.

GRAPHING STORIES:

Watch the video and graph the story.

Clock: www.graphingstories.com/2kj

GRAPHING STORIES:

Watch the video and graph the story.

Height of waist off ground: www.graphingstories.com/4my

5 x2 25

How would you use your calculator to solve 52?

The number you entered is the input number (or x-value on a graph).The result is the output number (or y-value on a graph).The x2 key illustrates the idea of a function.

InputInput OutputOutput

Press:Press:

A function is a relation that gives a single output number for every valid input number.A function is a relation that gives a single

output number for every valid input number.

There are many ways to represent relations:There are many ways to represent relations:

A relation is a rule that produces one or more output numbers for every valid input number.A relation is a rule that produces one or more output numbers for every valid input number.

These are all ways of showing a relationship between two

variables.

These are all ways of showing a relationship between two

variables.

GraphEquationTable of valuesA set of ordered pairsMapping

A function is a rule that gives a single output number for every valid input number.

A function is a rule that gives a single output number for every valid input number.

To help remember & understand the definition:

Think of your input number, usually your x-coordinate, as a letter.Think of your input number, usually your x-coordinate, as a letter.

Think of your output number, usually your y-coordinate, as a mailbox.Think of your output number, usually your y-coordinate, as a mailbox.

A function is a rule that gives a single output number for every valid input number.

A function is a rule that gives a single output number for every valid input number.

Input number Input number

Output number Output number

Can you have one letter going to two different mail boxes?Can you have one letter going to two different mail boxes?

Not a FUNCTIONNot a FUNCTION

A function is a rule that gives a single output number for every valid input number.

A function is a rule that gives a single output number for every valid input number.

Input number Input number

Output number Output number

Can you have two different letters going to one mail box?

Can you have two different letters going to one mail box?

Are these relations or functions?Are these relations or functions?

x y

x y1 52 63 74 6

1

2

3

4

1

2

3

4

5

6

7

5

6

7

Function &

Relation

Function &

Relation

Are these relations or functions?Are these relations or functions?

x y

x y1 52 61 71 6

1

2

1

2

5

6

7

5

6

7

Not a Function but a

Relation

Not a Function but a

Relation

xx yy

x y1 52 62 113 8

1

2

3

1

2

3

5

6

8

11

5

6

8

11

Not a functionBut a relationNot a functionBut a relation

Are these relations or functions?Are these relations or functions?

x y-2 -

1-1 1 0

3 1

5

x y-2 -

1-1 1 0

3 1

5

Double the number and add 3Double the number and add 3

As an equation:

In words:

y = 2x + 3y = 2x + 3

As a table of values:

As a set of ordered pairs:(-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3,

9)(-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9)

These all represent the

SAME function!

These all represent the

SAME function!

 

56

45

32

43

51

YX

We know it is a function because non of the “x” values in the table repeat. We can also hold a vertical line up to the points and see that no 2 points are touched by the same vertical line

This method of determining a function from a graph is know as the

vertical line test

#1

-22

-31

-40

-5-1

-6-2

YX

Is this a function?

Run vertical line across the graph and see if it touches two places at the same time

This is a function because it passes the vertical line test.

54

41

32

43

51

YX

#2

Notice the two points that are touched by the green line. This means that the relation is not a function

Functional NotationAn equation that is a function may be expressed using functional notation. The notation f(x) (read “f of (x)”) represents the variable y.

1. For the function f(x) = 2x + 6, the notation f(3) meansthat the variable x is replaced with the value of 3.

f(x) = 2x + 6f(3) = 2(3) + 6f(3) = 12

Functional Notation Con’t

(3, 12)

Given f(x) = 4x + 8, find each:f(2)

2. Evaluating Functions

= 4(2) + 8= 16

(2, 16)

If f(x) = 3x 1, and g(x) = 5x + 3, find each:

Evaluating More Functions

= [3x - 1] + [5x + 3]= 3x – 1 + 5x + 3= 8x + 2

= [3x - 1] - [5x + 3]= 3x – 1 – 5x - 3= -2x - 4

1. f(x) + g(x)

2. f(x) - g(x)