College Algebra
Name:
Guided Notes – Sec 1.1
Period:
3
5
Date: 8/24/10
Relation – a pairing of the elements of one set with the
elements of a second set, generally written as
a set of ordered pairs
Abscissa – the first element of an ordered pair
Domain – the set of all first elements (abscissas) in a
given relation (set of ordered pairs)
Ordinate – the second element of an ordered pair
Range – the set of all second elements (ordinates) in a
given relation (set of ordered pairs)
Example #1 – Rewrite the following set of data as a set
of ordered pairs. Then identify the domain and range.
Windchill Factors at 20o F
Wind
Speed
(mph)
Windchill
Temp
(o F)
5
10
15
20
25
30
19
3
-5
- 10
- 15
- 18
Relation:
{ (5, 19) , (10, 3) , (15, - 5) , (20, - 10) , (25, - 15) , (30, - 18) }
Domain:
{ 5, 10, 15, 20, 25, 30 }
Range:
{ 19, 3, –5, –10, –15, –18 }
Example #2: Rewrite the following relation as a set of
ordered pairs. Then identify the domain and range.
The domain of the relation is all integers from – 2 to 2,
inclusive. The range of the relation is 2 less than twice
each member of the domain.
First, identify the domain.
D = { - 2, - 1, 0, 1, 2 }
Next, identify the range.
Note: It may be helpful to set up a table of values.
x
-2
y = 2x – 2
= 2(-2) – 2 = - 6
-1
= 2(-1) – 2 = - 4
Thus, the range is …
0
= 2(0) – 2 = - 2
R = { - 6, - 4, - 2, 0, 2 }
1
= 2(1) – 2 = 0
2
= 2(2) – 2 = 2
That means the relation is the set of ordered pairs …
{ (- 2, - 6) , (- 1, - 4) , (0, - 2) , (1, 0) , (2, 2) }
Example #3: Determine the domain and range for each
of the following relations.
1.
2.
3.
4.
Each mark represents 5 units
D=
D=
All reals
R=
D=
All reals
R=
All reals
#>0
D=
–5 < # < 5
All reals
R=
–5 < # < 5
R=
#>0
How do graphs 3 and 4 “differ” from graphs 1 and 2?
Note: Think of your answer in terms of domain and/or range.
- In 3 and 4, there are values of the domain that …
are paired with more than one value of the range.
- In 1 and 2, the values of the domain …
never appear more than one time.
- In 3 and 4, you can draw
vertical
line(s) that …
intersect the graph in more than one point.
- In 1 and 2, you can draw
vertical line(s) that …
never intersect the graph in more than one point.
What term can we use to describe the relations
represented by the graphs in 1 and 2?
They represent functions.
Define a Function –
A function is a relation in which each element of the
domain is paired with exactly one element of the range.
Ex. #3 - Determine whether each relation is a function.
{ (1, 2) , (2, 3) , (3, 4) }
D=
R=
{1, 2, 3}
{2, 3, 4}
Function: Y
N
Yes
{1}
Function: Y
N
Yes
{ (1, 1) , (2, 1) , (3, 1) }
D=
R=
{1, 2, 3}
{ (1, 1) , (1, 2) , (1, 3) }
D=
R=
{1}
Function: Y
{1, 2, 3}
N
No
This tells us that in a function …
- No element of the domain … can be repeated.
- Elements of the range … may be repeated.
- If there are fewer elements in the domain then there are
in the range, then … the relation is NOT a function.