evaluating functions from graphs and tables sections 5.1 & 14.1c
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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
EXAMPLE 2: Use the graph of h(x) below to find the following values.
( 2)h
(0)h
2
What does y equal when
x = 0?
3
3
EXAMPLE 2: Use the graph of h(x) below to find the following values.
( 2)h
(0)h
(3)h
23
What does y equal when
x = 3?
1
1
EXAMPLE 2: Use the graph of h(x) below to find the following values.
( 2)h
(0)h
(3)h
(6)h
231
What does y equal when
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
What does y equal when
x = 10?16
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
What does y equal when
x = 2?
16
(2)f 8
( ) 2,4 , 0,8 , 3, 1 , 8,2g x
Example 3: Use the set of ordered pairs, table, or mapping to find the following.
(0)g
(8)g
What does y equal when
x = 0?
8
( ) 2,4 , 0,8 , 3, 1 , 8,2g x
Example 3: Use the set of ordered pairs, table, or mapping to find the following.
(0)g
(8)g
What does y equal when
x = 8?8
2
Example 3: Use the set of ordered pairs, table, or mapping to find the following.
x
( )h x
-5 -4 -1 0 2 3
5 -4 -4 7 0 -8
( 4)h
(3)h
What does y equal when
x = 8?
4
Example 3: Use the set of ordered pairs, table, or mapping to find the following.
x
( )h x
-5 -4 -1 0 2 3
5 -4 -4 7 0 -8
( 4)h
(3)h
What does y equal when
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