The document discusses functions and relations. It defines a relation as a rule that relates inputs from one set to outputs in another set, while a function relates each input to only one output. It provides examples of relations and functions. The key difference between relations and functions discussed is that a function pairs each input with only one output, while a relation can pair an input to multiple outputs. The document also discusses using functions to model real-life situations and how to represent functions graphically using a vertical line test.

1. CHAPTER 1 FUNCTIONS
Lesson 1: Functions as models
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2. LESSON 1: FUNCTIONS AS MODELS
The following table shows how relations and functions
are the same and how they are different.
@ReylkastroRey Lagrosa Castro @REYLKASTRO
A relation is a rule
that relates values
from a set of values
(called the domain)
to a second set of
values (called the
range)
A function is a
relation where
element in the
domain is related to
only one value in the
range by some rule.

3. LESSON 1: FUNCTIONS AS MODELS
The following table shows how relations and functions
are the same and how they are different.
@ReylkastroRey Lagrosa Castro @REYLKASTRO
A relation is a rule
that relates values
from a set of values
(called the domain)
to a second set of
values (called the
range)
A function is a
relation where
element in the
domain is related to
only one value in the
range by some rule.
Example:
f = {(1,3), (1,4), (2,5), (2,6), (3,7)}
h = {(1,3),(2,6),(3,9),...(n,3n),...}

4. LESSON 1: FUNCTIONS AS MODELS
The following table shows how relations and functions
are the same and how they are different.
Relation Function
@ReylkastroRey Lagrosa Castro @REYLKASTRO
The elements of the
domain can be
imagined as input to a
machine that applies a
rule to these inputs to
generate one or more
outputs.
The elements of the
domain can be
imagined as input to a
machine that applies a
rule so that each input
corresponds to only
one or outputs.

5. LESSON 1: FUNCTIONS AS MODELS
The following table shows how relations and functions
are the same and how they are different.
Relation Function
@ReylkastroRey Lagrosa Castro @REYLKASTRO
The elements of the
domain can be
imagined as input to a
machine that applies a
rule to these inputs to
generate one or more
outputs.
The elements of the
domain can be
imagined as input to a
machine that applies a
rule so that each input
corresponds to only
one or outputs.

6. LESSON 1: FUNCTIONS AS MODELS
The following table shows how relations and functions
are the same and how they are different.
Relation Function
@ReylkastroRey Lagrosa Castro @REYLKASTRO
A relation is also a set
of ordered pairs (x,y).
A function is a set of
ordered pairs (x,y)
such that no two
ordered have the same
x-value but different y-
values.

7. LESSON 1: FUNCTIONS AS MODELS
The following table shows how relations and functions
are the same and how they are different.
Relation Function
@ReylkastroRey Lagrosa Castro @REYLKASTRO
A relation is also a set
of ordered pairs (x,y).
A function is a set of
ordered pairs (x,y)
such that no two
ordered have the same
x-value but different y-
values.
x2 + y2 = 1

8. FUNCTIONS AND RELATIONS AS A TABLE OF
VALUES
Example 1. Which of the following relations
are functions?
a. f = {(1,2),(2,2),(3,5),(4,5)}
b. g = {(1,3),(1,4),(2,5),(2,6),(3,7)}
c. h = {(1,3),(2,6),(3,9), ... (n,3n),...}
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9. FUNCTIONS AND RELATIONS AS A TABLE OF
VALUES
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Example 2. Which of the following mapping
diagrams represent functions?

10. FUNCTIONS AS A GRAPH IN THE CARTESIAN
PLANE
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The Vertical Line Test
A graph represents a function if and only if each
vertical line intersects the graph at most once.

11. DOMAIN OF A RELATION
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12. FUNCTIONS AS REPRESENTATIONS OF REAL-
LIFE SITUATIONS
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Functions can often be used to model real life situations.

13. FUNCTIONS AS REPRESENTATIONS OF REAL-
LIFE SITUATIONS
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Functions can often be used to model real life situations.

14. PIECEWISE FUNCTIONS
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16. ASSIGNMENT