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

EVALUATING FUNCTIONS FROM GRAPHS AND TABLES
SECTIONS 5.1 & 14.1C
Function notation replaces the independent variable, y
with either f(x), g(x), or h(x).
f _____
of _____”
x
f(x) is read as “ ____
Does not mean
multiplication!
g _____
of _____”
x
g(x) is read as “ ____
h _____
of _____”
x
h(x) is read as “ ____
EXAMPLE 1: If
g ( x)  x 2  3
Find
g (4)   4   3
2
g (4)  16  3
g (4)  19
g (4)
EXAMPLE 2: Use the graph of h(x) below to find the following
values.
h(2) 
2
2
What does
y equal
when
x = -2?
EXAMPLE 2: Use the graph of h(x) below to find the following
values.
h(2) 
h(0) 
3
2
3
What does
y equal
when
x = 0?
EXAMPLE 2: Use the graph of h(x) below to find the following
values.
h(2) 
h(0) 
2
3
h(3) 
1
1
What does
y equal
when
x = 3?
EXAMPLE 2: Use the graph of h(x) below to find the following
values.
h(2) 
7
h(0) 
2
3
h(3) 
1
h(6) 
7
What does
y equal
when
x = 6?
Try these…
Use the graph of
h( x )
below to find the following values.
h(4) 
2
h(0) 
3
h(2) 
3
h(5) 
3
Example 3: Use the set of ordered pairs, table,
or mapping to find the following.
What does
y equal
Domain
Range
when
f ( x)
x = 10?
2
8
5
11
10
16
f (10)  16
Example 3: Use the set of ordered pairs, table,
or mapping to find the following.
Domain
Range
f ( x)
2
8
5
11
10
16
f (10)  16
f (2)  8
What does
y equal
when
x = 2?
Example 3: Use the set of ordered pairs, table,
or mapping to find the following.
What does
y equal
when
x = 0?
g ( x)   2,4 ,  0,8 , 3, 1 , 8,2 
g (0) 
g (8) 
8
Example 3: Use the set of ordered pairs, table,
or mapping to find the following.
g ( x)   2,4 ,  0,8 , 3, 1 , 8,2 
What does
y equal
when
x = 8?
g (0) 
8
g (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
What does
y equal
when
x = 8?
h(4) 
h(3) 
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
What does
y equal
when
x = 3?
h(4) 
4
h(3) 
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
1
1
1
Y
1
12
2
16
3
20
4
24
5
28
6
32
7
36
8
40
4
4
Look for a pattern in the range >
4
Look for a pattern in the domain >
1
4
Set it up as a ratio of range to domain >
This is your cost per hour (rental fee).
$4.00 per hour
4
4
1
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
1
Y
$4.00 per hour
12
2
16
3
20
4
24
5
28
6
32
7
36
8
40
If the total cost to rent the bike for 1 hour
is $12, and it cost ______
$4 per hour, your
initial deposit must have been ________.
$8
Total cost  cost per hour  initial deposit
y  4x  8
f ( x)  4 x  8
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.
1 1 1
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
Time in hours, x
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…
Total cost = cost per hour + deposit
f ( x)  5 x  10
$10
The equation
f ( x)  13x  26
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?
$13
$26
The equation
f ( x)  13x  26
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 .
f ( x)
dependent
is called the _______________
variable.
x
independent variable
is called the ________________
On a graph,
horizontal
the independent variable is on the ________________
axis
vertical
and dependent variable is on the _______________
axis.
dependent
independent
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. 1 1 1
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
4 4 4
Domain: {1, 2,3, 4,5, 6, 7,8}
Range:
{12,16, 20, 24, 28,32,36, 40}
f ( x)  4 x  8
12  4  8
f ( x)  4 x  8
40

30



20
10



1

2
3
4
5
6
7
8