2­1 Relations and Functions 2010
September 10, 2010
{(2,0),
(4,1), (
3,­5)}
y=
(3
x+
2)
/(
4x
­1)
2.1 Relations & Functions
Objective:
Graph
relations & identify functions.
Th
e num
the am ber of wid
ge
ount o
f cons ts produce
d
tructio
n mate at a widge
t f
rial av
ailable actory is pa
. If the
rt
re are ly depende
4.2 m
n
illion . t on ..
3
5
5
0
­1
5
Sep 16 ­ 12:40 PM
1
2­1 Relations and Functions 2010
September 10, 2010
Check Skills You'll Need
Graph each ordered pair on the coordinate plane.
1. A (­4, ­8)
2. B (3, 6)
3. C (0, 0)
4. D (­1, 3)
5. E (­6, 5)
Evaluate each expression for x = ­1, 0, 2, and 5
2
6. 2x + 1
7. | x ­ 3 |
Sep 16 ­ 12:47 PM
2
2­1 Relations and Functions 2010
September 10, 2010
h
c
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ic
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on e dom in the
i
t
c
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h
t
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o
A
t m
n
e
l
e
e
elem tly one
c
exa
Sep 16 ­ 12:47 PM
3
2­1 Relations and Functions 2010
September 10, 2010
Are the following examples of functions?
1
2
Dec
The price of a ski lift ticket is Jan
related to which month you wish Feb
Mar
to ski.
Apr
y = 3x
2
$37
$42
$50
$50
$44
-4
squips
3
4
borks
A
b
1
2
3
4
A
B
C
Teacher explanation:
While this IS a function, it is not a one­to­one function. In a one­
to­one function, each member of the range "comes from" only one member of the domain.
Sep 16 ­ 12:44 PM
4
2­1 Relations and Functions 2010
September 10, 2010
Vertical Line Test
If a vertical line passes through at least two points on the graph, then one element of the domain is paired with more than one element of the range. Therefore the relation is not a function.
Examples:
Sep 16 ­ 12:47 PM
5
2­1 Relations and Functions 2010
September 10, 2010
A function rule expresses an output value in terms of an input value.
Examples of function rules
input
y = 2x
output
input
input
f(x) = x + 5
output
C = d
output
Sep 16 ­ 12:47 PM
6
2­1 Relations and Functions 2010
September 10, 2010
Reading function notation
y = 3x + 2
f(x) = 3x + 2
3 facts:
f(x) is pronounced "f of x"
"a function f of x"
f(x) does not mean "f times x"
Sep 16 ­ 12:47 PM
7
2­1 Relations and Functions 2010
Input
Function
September 10, 2010
Output
Ordered pair
5
Subtract 1
4
(4, 5)
a
Add 2
a + 2
(a, a + 2)
3
g
g(3)
(3, g(3))
x
f
f(x)
(x, f(x))
Sep 16 ­ 12:47 PM
8
2­1 Relations and Functions 2010
September 10, 2010
Sep 10­10:25 AM
9
2­1 Relations and Functions 2010
September 10, 2010
real world connection
The area of a square tile is a function of the length of a side of the square. Write a function rule for the area of a square.
2
Relate:
area of a square is (side length)
Define:
Let s = the length of one side of the square tile.
Then A(s) = the area of the square tile
Write:
A(s) = s 2
Sep 9 ­ 12:17 PM
10
2­1 Relations and Functions 2010
September 10, 2010
Sep 10­10:31 AM
11
2­1 Relations and Functions 2010
September 10, 2010
real world connection
The area of a square tile is a function of the length of a side of the square. Write a function rule for the area of a square.
Evaluate the function for a square with side length 3.5 in.
A(s) = s 2
2
A(3.5) = (3.5)
= 12.25
Substitute 3.5 for s.
Simplify.
Sep 9 ­ 12:17 PM
12
2­1 Relations and Functions 2010
September 10, 2010
Evaluating Functions
Given the function:
a) Find f(2)
b) Find f(­4)
c) Find f(a+b)
Sep 9 ­ 12:17 PM
13
2­1 Relations and Functions 2010
September 10, 2010
Homework
pg. 59 ­ 60
#'s: 12 ­ 54 even, 62 ­ 65
Sep 12 ­ 9:05 AM
14