Chapter 3 Section 8

1
Chapter 3 Section 8

• Introduction to Functions

2
Rules of Correspondence

• We often use a rule to relate how the first value
  of an ordered pair relates to the second one.

Rule
x
y
Domain
Range
3
Example
4
Definition of a Relation

• A Relation maps a value from the domain to the
  range. A Relation is a set of ordered pairs.
• The most common types of relations in algebra,
  map subsets of real numbers to other subsets of
  real numbers.

5
Definition of a Relation
6
Relation
(A)
(B)
(C)

• 36 mpg
• 8 mpg
• 16 mpg

7
Definition of a Function

• If a relation has the additional characteristic
  that each element of the domain is mapped to one
  and only one element of the range then we call
  the relation a Function.

8
Definition of a Function

• If we think of the domain as the set of boys and
  the range the set of girls, then a function is a
  monogamous relationship from the domain to the
  range. Each boy gets to go out with one and only
  one girl.
• But It does not say anything about the girls.
  They get to live in Utah.

9
Examples

• Decide if the following relations are functions.

10
Ways to Represent a Function

• Algebraic

• Graphical

• Numeric

• DescriptiveThe cost is twice the original amount.

11
Pieces of a Function

• A function consists of 3 parts1. a set of
  objects called the domain2. a second set of
  objects called the range3. And a rule that
  describes how to assign a unique range object to
  each object in the domain.

12

• The Coffee
• On the way to work each day, professor Olsen
  stops his vintage Volvo wagon at Jitter Bean and
  purchases the first of his needed caffeine
  ingestions. Since he is a parent, the number of
  cups of coffee that he consumes through his busy
  day varies, depending mostly upon how many hours
  his young son slept through the night.

13

• There are three pieces to the previous paragraph
  the number of hours professor Olsens son slept
  (the domain), the number of cups of coffee during
  the day Professor consumes during the day (the
  range), and the rule between them. We can infer
  that the rule is the less hours professor
  Olsens son sleeps, the more cups of coffee he
  drinks.
• Another way to see a function is in a graph. Use
  the following graph as the rule to connect values
  from the set of inputs (the domain) and the set
  of outputs (the range)

14
(No Transcript)
15
Vertical Line Test

• If a vertical line crosses a graph more than
  once, then the graph is not a function.
• Page 269 45-52

16
Determine Domain Range from Graph
17
Function Notation
18
Examples of Function Notation

• Using the notation to evaluate the functions
• f(2), g(-1), f(-0.9), g(3), g(2t),
  f(a2),

19
Examples

• Page 268 21, 25, 29