2 1 .
Graphs
* on a number line each point represents a number
8
-
...
, y
- ...
S >
Consider number lines perpendicular to each other
M
E Defines plane a .
... - ..... write coordinates as (X Y), .
F Order Pair (X Y)
,
that each
point in this plane corresponds
( )
+ 11 1(+ ,+)
to
-
,
.
horizontal line is the X-axis .
vertical line is the y-axis
0
.
the plane defined
by them
is the Xy-plane .
Locate the origin (0 0). ,
( -) -)
(2 3) (3 2) (2 5 0
Ill NV +,
Locate
,
,
.
, , , ,
-
4 regions/quadrants
o labelled counterclockwise.
, .1
2 Graphs Continuation :
Example : y
= X
, y 2x 1,
= -
3y =
10x+ 3
A solution to the
equation is any ordered pair
·
(a b) ,
for which the equation holds true ..
Ex : check whether (4 2) ,1 , -4)
, ,
and (2 5) , are
solutions of y =
3x-1 .
a (4, 2) (2 + 3(4) 1 - =
11
not a solution.
b( 1 4) - -
3 -
4 = 30 -
1 -
1 = -
4
it is a solution.
c 2, 5 75 = 32 -
1 = 5
it is a solution.
Ex2 y : =
2x + 1 > How
many solutions does it
have? infinite solutions
9 make a table to check.
X y 2x 1(X Y) D For
every X-value , there is a
corresponding
= -
,
0 20 -1 (0 -1)
,
y-values·
1 201 -1 (1 , 1 C
graph solutions found.
33 2 . -
13, 3
1 2 1
T 7
-1 - . -
-
1 ,-3
4
-r
4
2
10 8 - 6 4 I 810
-
4
-
-
2
-
Z
-
2
4
-
6
-
8
L
, X Y= -
2x(X ) ,
Ex3 :
Graph y =
-2 x .
-
2 -
20 2 -
-
2 ,
4
I 10 2
T 1
-
2
- -
-
,
X
4
O -
2 0 -
0, 0
↓ 2 /
O 4 - -
1 .
-2
2
· 2
2 Z
;-4
-
2
:
①
10 8 - 6 4 6810
-
4
-
-
22
-
-
2
-
4 ⑧
-
6
V
-
8
Ex4 x2 Xy = x2 1(x, Y)
:
Graph y = -
1
()
T
-
2 (-2)? -
1 ( 2 3)
-
,
N
4
1
- -,
(- , 0
O (
4
6
2
·
&
22
10-8 -4 4 24 6010
-
1 (2 , 3)
-
-
2
-
i
-
6
-
8
.2 Functions :
2
Example: To each person in class has a date of birth .
Example : To each car in Indianapolis has its own license plate
.
What is a function?
·
a correspondence between a first set, called the domain ,
and a second set, called the range , where each
member of the domain is matched to
exactly one
member of the range.
ounique connection
Graphs
* on a number line each point represents a number
8
-
...
, y
- ...
S >
Consider number lines perpendicular to each other
M
E Defines plane a .
... - ..... write coordinates as (X Y), .
F Order Pair (X Y)
,
that each
point in this plane corresponds
( )
+ 11 1(+ ,+)
to
-
,
.
horizontal line is the X-axis .
vertical line is the y-axis
0
.
the plane defined
by them
is the Xy-plane .
Locate the origin (0 0). ,
( -) -)
(2 3) (3 2) (2 5 0
Ill NV +,
Locate
,
,
.
, , , ,
-
4 regions/quadrants
o labelled counterclockwise.
, .1
2 Graphs Continuation :
Example : y
= X
, y 2x 1,
= -
3y =
10x+ 3
A solution to the
equation is any ordered pair
·
(a b) ,
for which the equation holds true ..
Ex : check whether (4 2) ,1 , -4)
, ,
and (2 5) , are
solutions of y =
3x-1 .
a (4, 2) (2 + 3(4) 1 - =
11
not a solution.
b( 1 4) - -
3 -
4 = 30 -
1 -
1 = -
4
it is a solution.
c 2, 5 75 = 32 -
1 = 5
it is a solution.
Ex2 y : =
2x + 1 > How
many solutions does it
have? infinite solutions
9 make a table to check.
X y 2x 1(X Y) D For
every X-value , there is a
corresponding
= -
,
0 20 -1 (0 -1)
,
y-values·
1 201 -1 (1 , 1 C
graph solutions found.
33 2 . -
13, 3
1 2 1
T 7
-1 - . -
-
1 ,-3
4
-r
4
2
10 8 - 6 4 I 810
-
4
-
-
2
-
Z
-
2
4
-
6
-
8
L
, X Y= -
2x(X ) ,
Ex3 :
Graph y =
-2 x .
-
2 -
20 2 -
-
2 ,
4
I 10 2
T 1
-
2
- -
-
,
X
4
O -
2 0 -
0, 0
↓ 2 /
O 4 - -
1 .
-2
2
· 2
2 Z
;-4
-
2
:
①
10 8 - 6 4 6810
-
4
-
-
22
-
-
2
-
4 ⑧
-
6
V
-
8
Ex4 x2 Xy = x2 1(x, Y)
:
Graph y = -
1
()
T
-
2 (-2)? -
1 ( 2 3)
-
,
N
4
1
- -,
(- , 0
O (
4
6
2
·
&
22
10-8 -4 4 24 6010
-
1 (2 , 3)
-
-
2
-
i
-
6
-
8
.2 Functions :
2
Example: To each person in class has a date of birth .
Example : To each car in Indianapolis has its own license plate
.
What is a function?
·
a correspondence between a first set, called the domain ,
and a second set, called the range , where each
member of the domain is matched to
exactly one
member of the range.
ounique connection
