DATE
NAME
5-1
Student Edition
Pages 254–259
Study Guide
The Coordinate Plane
y
In the diagram at the right, the two perpendicular
lines, called the x-axis and the y-axis, divide the
coordinate plane into Quadrants I, II, III, and IV. The
point where the two axes intersect is called the origin.
The origin is represented by the ordered pair (0, 0).
Every other point in the coordinate plane is also
represented by an ordered pair of numbers. The
ordered pair for point Q is (5, 24). We say that 5 is the
x-coordinate of Q and 24 is the y-coordinate of Q.
II
5
R
4
3
2
1
–5 –4 –3 –2 –1O
–1
–2
III
I
1 2
3
–3
–4
IV
4 5 x
Q
(5, –4)
–5
Example: Write the ordered pair for the point R above.
The x-coordinate is 0 and the y-coordinate is 4. Thus,
the ordered pair for R is (0, 4).
To graph any ordered pair (x, y), begin at the origin. Move left or
right x units. From there, move up or down y units. Draw a dot
at that point.
y
Graph each point on the coordinate plane at the right.
1. A (0, 0)
2. B (5, 0)
3. C (23, 4)
4. D (4, 25)
5
4
3
2
1
5. E (22, 23)
6. F (2, 21)
–5 –4 –3 –2 –1O
–1
J
–2
I
–3
–4
Write the ordered pair for each point shown at the right.
Name the quadrant in which the point is located.
7. G
8. H
© Glencoe/McGraw-Hill
9. I
–5
H
1 2
3
4 5 x
G
10. J
34
Algebra 1
DATE
NAME
5-2
Student Edition
Pages 262–269
Study Guide
Relations
A relation is a set of ordered pairs. The domain of a relation is
the set of all first coordinates of the ordered pairs, and the
range is the set of all second coordinates.
Example 1: State the domain and range of each relation.
1. {(3, 3), (3, 4), (3, 5)} Domain 5 {3}; Range 5 {3, 4, 5}
2. {(1, 2), (2, 1), (3, 2)} Domain 5 {1, 2, 3}; Range 5 {1, 2}
Relations may be expressed in the form of ordered pairs, tables,
graphs, and mappings.
Example 2: The relation {(1, 1), (0, 2), (3, 22)} can be expressed
in each of the following ways.
Ordered pairs
(1, 1)
(0, 2)
(3, 22)
Table
x
y
1
1
0
2
3
22
Graph
y
Mapping
y
x
x
O
1
0
3
1
2
–2
The inverse of any relation is obtained by switching the
coordinates in each ordered pair.
State the domain and range of each relation.
1. {(26, 5), (23, 8), (26, 9), (3, 11)}
2. {(0.8, 20.8), (1.2, 0), (3.5, 4)}
3.
{(12, 14), (112, 114), (312, 2)}
Express the relations shown in each table, mapping, or graph as a set of ordered
pairs. Then state the domain, range, and inverse of the relation.
4.
x
y
1
3
2
4
3
6
5. x
y
6
2
1
0
3
4
5
Draw a mapping and graph for each relation.
6. {(22, 21), (3, 3), (4, 3)}
© Glencoe/McGraw-Hill
7. {(0, 0), (1, 1), (2, 2)}
35
Algebra 1
DATE
NAME
5-1
Student Edition
Pages 254–259
Study Guide
The Coordinate Plane
y
In the diagram at the right, the two perpendicular
lines, called the x-axis and the y-axis, divide the
coordinate plane into Quadrants I, II, III, and IV. The
point where the two axes intersect is called the origin.
The origin is represented by the ordered pair (0, 0).
Every other point in the coordinate plane is also
represented by an ordered pair of numbers. The
ordered pair for point Q is (5, 24). We say that 5 is the
x-coordinate of Q and 24 is the y-coordinate of Q.
5
R
4
3
2
1
II
–5 –4 –3 –2 –1O
–1
–2
I
1 2
3
–3
–4
III
4 5 x
Q
IV
(5, –4)
–5
Example: Write the ordered pair for the point R above.
The x-coordinate is 0 and the y-coordinate is 4. Thus,
the ordered pair for R is (0, 4).
To graph any ordered pair (x, y), begin at the origin. Move left or
right x units. From there, move up or down y units. Draw a dot
at that point.
y
Graph each point on the coordinate plane at the right.
I
1. A (0, 0)
2. B (5, 0)
3. C (23, 4)
4. D (4, 25)
5. E (22, 23)
–5 –4 –3 –2 –1O
–1
J
–2
E
–3
–4
6. F (2, 21)
Write the ordered pair for each point shown at the right.
Name the quadrant in which the point is located.
7. G
(0, 25);
none
8. H
© Glencoe/McGraw-Hill
(2, 3);
I
9. I
C
5
4
3
2
1
–5
H
A
1 2 3
F
G
B
4 5 x
D
10. J
(24, 4);
II
T34
(23, 22);
III
Algebra 1
DATE
NAME
5-2
Student Edition
Pages 262–269
Study Guide
Relations
A relation is a set of ordered pairs. The domain of a relation is
the set of all first coordinates of the ordered pairs, and the
range is the set of all second coordinates.
Example 1: State the domain and range of each relation.
1. {(3, 3), (3, 4), (3, 5)} Domain 5 {3}; Range 5 {3, 4, 5}
2. {(1, 2), (2, 1), (3, 2)} Domain 5 {1, 2, 3}; Range 5 {1, 2}
Relations may be expressed in the form of ordered pairs, tables,
graphs, and mappings.
Example 2: The relation {(1, 1), (0, 2), (3, 22)} can be expressed
in each of the following ways.
Ordered pairs
(1, 1)
(0, 2)
(3, 22)
Table
x
y
1
1
0
2
3
22
Graph
y
Mapping
y
x
x
O
1
0
3
1
2
–2
The inverse of any relation is obtained by switching the
coordinates in each ordered pair.
State the domain and range of each relation.
1. {(26, 5), (23, 8), (26, 9), (3, 11)} D 5 {26, 23, 3}; R 5 {5, 8, 9, 11}
2. {(0.8, 20.8), (1.2, 0), (3.5, 4)} D 5 {0.8, 1.2, 3.5}; R 5 {20.8, 0, 4}
3.
1 1
,
2 4
{( ) (
1
1
)(
1
)}
, 12, 14 , 32, 2
D5
{ , 1 , 3 }; R 5 { , 1 , 2}
1
2
1
2
1
2
1
4
1
4
Express the relations shown in each table, mapping, or graph as a set of ordered
pairs. Then state the domain, range, and inverse of the relation.
4.
x
y
1
3
2
4
3,
6
{(1, 3), (2, 4), (3, 6)}
5. x
6
D 5 {1, 2, 3}
2
R 5 {3, 4, 6}
I 5 {(3, 1), (4, 2), (6, 3)}
1
0
y
3
4
5
{(6, 5), (2, 3), (1, 4), (0, 3)}
D 5 {0, 1, 2, 6}
R 5 {3, 4, 5}
I 5 {(5, 6), (3, 2), (4, 1),
(3, 0)}
Draw a mapping and graph for each relation.
6. {(22, 21), (3, 3), (4, 3)}
x
y
–2
–1
3
3
4
© Glencoe/McGraw-Hill
7. {(0, 0), (1, 1), (2, 2)}
x
y
0
0
1
1
2
2
y
O
x
T35
y
O
x
Algebra 1