CHAPTER 1: LINEAR
RELATIONS AND
FUNCTIONS
SECTION 1-1
Relations and Functions
Objectives
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Determine whether a given relation is a
function
Identify the domain and range of a relation or
function
Evaluate functions
What is a relation?
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A pairing of elements of one set with elements
of a second set is called a relation.
The first element of an ordered pair is the
abscissa.
The second element of an ordered pair is the
ordinate.
The set of abscissas is called the domain and
the set of ordinates is called the range of a
relation.
Example 1
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„
State the relation of the
windchill data as a set
of ordered pairs. Also
state the domain and
range of the relation.
Answer:
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(5,19), (10,3), (15,-5), (20,-10),
(25,-15), (30,-18)
D = 5, 10, 15, 20, 25, 30
R = 19, 3, -5, -10,-15,-18
Wind Speed
(mph)
5
10
15
20
25
30
Windchill
Temperature (F)
19
3
-5
-10
-15
-18
Example 2
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The domain of a relation
is all consecutive
integers between -2 and
2. The range y of the
relation is 2 less than
twice x, where x is a
member of the domain.
Write the relation as a
table of values and as an
equation. Then graph
the relation.
x
-1
0
1
Equation: y = 2x – 2
y
-4
-2
0
Example 3
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State the domain and range of the relation
D = all real numbers
R = all negative numbers and zero
A function is a relation in which
each element of the domain is paired
with exactly one element of the
range.
Function: One to One ( Every x has a different y)
Example: y = 3x -5
Function: One to Many (Several x ’s have the same y)
Example: y = x 2
NOT A FUNCTION IS MANY TO ONE!!
EXAMPLE: x = y 2
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Vertical Line Test
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If a vertical line drawn on the graph of a
relation passes through no more than one point
of the graph, then the relation is a function.
This is called the vertical line test.
Function Notation
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Any letter may be used to denote a function. In
function notation, the symbol f(x) is read f of x
and is the value of the function f at x. X is
called the independent variable and y is called
the dependent variable because the value of y
depends upon what x you put in to the
function.
Homework
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HW#1
Section 1-1 Pp.10-12
#17, 18, 20, 21, 24, 25, 26, 29, 31, 33, 38, 39,
41, 45, 55, 57