2­1 Relations and Functions web.notebook
September 08, 2008
­1)
What is a Function?
(4,1), (
3,­5)}
y=
(3
x
+2
)/(
4x
{(2,0),
3
The n
u
the a mber of w
moun
t of c idgets pro
onstr
uctio duced at a
n ma
terial widget f
a
avail
able. ctory is p
If th
ere a artly depe
re 4.2
n
milli dent on 5
on ...
5
0
­1
5
Sep 16 ­ 12:40 PM
1
2­1 Relations and Functions web.notebook
September 08, 2008
Check Skills You'll Need
Graph each ordered pair on the coordinate plane.
1. (­4, ­8)
2. (3, 6)
3. (0, 0)
4. (­1, 3)
5. (­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 web.notebook
September 08, 2008
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Sep 16 ­ 12:47 PM
3
2­1 Relations and Functions web.notebook
September 08, 2008
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 web.notebook
September 08, 2008
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 web.notebook
September 08, 2008
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 web.notebook
September 08, 2008
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
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2­1 Relations and Functions web.notebook
Input
Function
September 08, 2008
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
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2­1 Relations and Functions web.notebook
September 08, 2008
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
9
2­1 Relations and Functions web.notebook
September 08, 2008
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
10
2­1 Relations and Functions web.notebook
September 08, 2008
Evaluating Functions
Given the function:
a) Find f(2)
b) Find f(­4)
c) Find f(a+b)
Sep 9 ­ 12:17 PM
11
2­1 Relations and Functions web.notebook
September 08, 2008
Homework
pg. 59 ­ 60
#'s: 12 ­21, 26­54 even, 62 ­ 65
Sep 12 ­ 9:05 AM
12