EVALUATING FUNCTIONS FROM GRAPHS AND TABLES SECTIONS 5.1 & 14.1C.

EVALUATING FUNCTIONS FROM GRAPHS AND TABLES

SECTIONS 5.1 & 14.1C

Does not mean multiplication!

Function notation replaces the independent variable, y with either f(x), g(x), or h(x).

f(x) is read as “ ____ _____ _____”

g(x) is read as “ ____ _____ _____”

h(x) is read as “ ____ _____ _____”

f of x

g of x

h of x

EXAMPLE 1: If 2( ) 3g x x Find (4)g

2( 34) 4g

( 34) 16g

( 14) 9g

EXAMPLE 2: Use the graph of h(x) below to find the following values.

( 2)h

What does y equal when

x = -2?

2

2


( 2)h

(0)h

2


x = 0?

3

3


( 2)h

(0)h

(3)h

23


x = 3?

1

1


( 2)h

(0)h

(3)h

(6)h

231


x = 6?

7

7

Try these…Use the graph of ( )h x below to find the following values.

( 4)h

(0)h

(2)h

(5)h

2

3

3

3

Example 3: Use the set of ordered pairs, table, or mapping to find the following.

2

5

10

8

11

16

Domain Range

( )f x

(10)f


x = 10?16


2

5

10

8

11

16

Domain Range

( )f x

(10)f


x = 2?

16

(2)f 8

( ) 2,4 , 0,8 , 3, 1 , 8,2g x


(0)g

(8)g


x = 0?

8

( ) 2,4 , 0,8 , 3, 1 , 8,2g x


(0)g

(8)g


x = 8?8

2


x

( )h x

-5 -4 -1 0 2 3

5 -4 -4 7 0 -8

( 4)h

(3)h


x = 8?

4


x

( )h x

-5 -4 -1 0 2 3

5 -4 -4 7 0 -8

( 4)h

(3)h


x = 3?

4

8

A table of values can help you to determine a rule for a linear function.

The table below shows the amount that a company charges for bicycle rental for up to 8 hours. An initial deposit is included in the amounts. Write an equation for the function.

X Y

1 12

2 16

3 20

4 24

5 28

6 32

7 36

8 40

Look for a pattern in the range >

Look for a pattern in the domain >

44

4

41

11

1

Set it up as a ratio of range to domain >This is your cost per hour (rental fee).

44

1

$4.00 per hour

A table of values can help you to determine a rule for a linear function.

The table below shows the amount that a company charges for bicycle rental for up to 8 hours. An initial deposit is included in the amounts. Write an equation for the function.

X Y

1 12

2 16

3 20

4 24

5 28

6 32

7 36

8 40

$4.00 per hour

If the total cost to rent the bike for 1 hour is $12, and it cost ______ per hour, your initial deposit must have been ________.

$4$8

Total cost cost per hour initial deposit

4 8y x

( ) 4 8f x x

The table below shows the amount that a company charges for a raft rental for up to 10 hours. An initial deposit is included in the amounts shown. Write an equation for the function.

Time in hours, x 1 2 3 4 5 6 7 8 9 10

Rental cost in dollars, f(x) 15 20 25 30 35 40 45 50 55 60

1 1 1

5 5 5

If the total cost to rent the raft for 1 hour is $15, and it cost $5 per hour, your initial deposit must have been…

$10Total cost = cost per hour + deposit

( ) 5 10f x x

The equation ( ) 13 26f x x shows the costs associated with being a member of a DVD club that charges a membership fee.

x = the number of CDs purchased and

( )f x = the total cost

How much is the membership fee?

What is the cost per DVD?

$26

$13

The equation ( ) 13 26f x x shows the costs associated with being a member of a DVD club that charges a membership fee.

x = the number of CDs purchased and

( )f x = the total cost

Linear equations contain an independent variable and a dependent variable.

The total cost ( )f x depends on the number of CD purchased x .

is called the ________________ variable

( )f x is called the _______________ variable.

x

dependent

independent

On a graph,

the independent variable is on the ________________ axis

and dependent variable is on the _______________ axis.

independent

dependent

horizontal

vertical

The table below shows the amount that a company charges for bicycle rental for up to 8 hours. 1. List the domain and range. 2. Write an equation for the function. 3. Graph the function.

Time in hours, x 1 2 3 4 5 6 7 8

Rental cost in dollars, f(x) 12 16 20 24 28 32 36 40

Domain: {1,2,3,4,5,6,7,8}

Range: {12,16,20,24,28,32,36,40}

4 4 4

1 1 1

( ) 4f x x 12 4 8

8

( ) 4 8f x x

10

20

40

30

1 2 3 4 5 6 7 8

EVALUATING FUNCTIONS FROM GRAPHS AND TABLES SECTIONS 5.1 & 14.1C.

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