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Title: Introducing Functions


1
Chapter 1 Introducing Functions
2
Definition (page 13) A function is a relationship
between two sets, the domain and the range, such
that each member of the domain corresponds to
exactly one member of the range. The domain is
the set of inputs that make sense for the
function The range is the set of outputs that can
be expected from the function.
3
Section 1.1 Defining Functions
A function can be expressed using Formula
Table Graph
1 Shoe Size
2 River Level
3 Z function
4
Example 1 Shoe Size(formula)
Your shoe size is certainly related to the size
of your foot. In fact, a shoe salesperson might
say that your shoe size is a function of or
depends on the length of your foot. For a
womans foot, we use the following formula which
tells specifically how to convert x, the length
in inches of a womans foot, into y, the number
giving her shoe size y 3x 21 (or S 3L
21) (In words, measure the length of a womans
foot in inches, multiply this measurement by 3
and subtract 21.) For a mans foot, we use the
following formula which tells specifically how to
convert x, the length in inches of a mans foot,
into y, the number giving his shoe size y 3x
22.5 (or S 3L -21) (In words, measure the
length of a mans foot in inches, multiply this
measurement by 3 and subtract 22.5.)
5
Example 1 Shoe Size (formula)
Function Notation
y 3x -21 w(x) 3x - 21
y 3x - 22.5 m(x) 3x 22.5
Allows us to refer to function by
name. Emphasizes the role of the input/output
variables.
w(9)6 A woman whose foot measures 9 inches wears
a size 6 shoe
6
Example 1 Shoe Size (table)
Create a table of values for w.
Create a table of values for m.
7
Example 1 Shoe Size (graph)
Graph the shoe size functions w and m.
8
Example 2 River Level (table)
Function Notation x variable day in April y
variable river level (in feet above sea
level) C(x)
C(10) 111.1 The river level on April 10 was
111.1 feet above sea level
9
Example 2 River Level (graph)
10
Example 2 River Level (graph)
C(14.5) 113
11
Example 3 Z function (graph)
What is Z(4)? What is Z(0)? For what input values
does Z(u) 10?
12
Section 1.2Using Functions to Model the Real
World
Consider w(x) 3x 21.
as a shoe function as a shoe function as a shoe function as a shoe function
Input Makes Sense? Output Makes Sense?
5 Yes -6 No
0 No
-5 No
12 Yes 15 No
as an abstract function as an abstract function as an abstract function as an abstract function
Input Makes Sense? Output Makes Sense?
5 Yes -6 Yes
0 Yes -21 Yes
-5 Yes -36 Yes
12 Yes 15 Yes
Domain all real numbers Range all real numbers
Domain legal foot measurements? Range legal
shoe sizes?
13
Section 1.2Using Functions to Model the Real
World
Consider w(x) 3x 21.
as a shoe function as a shoe function as a shoe function as a shoe function
Input Makes Sense? Output Makes Sense?
5 Yes -6 No
0 No
-5 No
12 Yes 15 No
discrete
Range (legal womens shoe sizes) 5, 5.5, 6,
6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10, 10.5, 11,
11.5,12, 12.5, 13
Domain (legal womens foot measurements) 5 3x
21 138.66 inches x 11.33 inches
continuous
14
Section 1.2 Using Functions to Model the Real
World
Examples from pages 12 and 13
15
Definition (page 13) A function is a relationship
between two sets, the domain and the range, such
that each member of the domain corresponds to
exactly one member of the range. The domain is
the set of inputs that make sense for the
function The range is the set of outputs that can
be expected from the function.
Example (pp14/15) Input square of a
number. Output number that was squared to get
the input.
Input Output
0
1
4
9
16
More Practice
11/32, 12/32 and 24/33
Homework Page 31 1-24 Turn in 14, 16, 20,24
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