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Over Lesson 1–3
A. A
B. B
C. C
D. D
A. Multiplicative IdentityB. Additive IdentityC. Associative Property of AdditionD. Associative Property of Multiplication
Name the property shown by the statement (4b)c = 4(bc).
Name the property shown by the statement 4y + 0 = 4y.
A. Multiplicative IdentityB. Additive IdentityC. Commutative Property of AdditionD. Associative Property of Addition
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You have already graphed numbers on number lines. (Previous Course)
• Use ordered pairs to locate points.
• Use graphs to represent relations.
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• coordinate system
• coordinate plane
• y-axis
• origin
• x-axis
• ordered pair
• x-coordinate
• y-coordinate
• graph
• relation
• domain
• range
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What is the coordinate plane?
• It is two intersecting lines drawn to find locations• These intersecting lines are the x-axis
(horizontal axis) and the y-axis (vertical axis)• These locations are called ordered pairs. An
ordered pair is written as its x-value and its y-value or (x,y)
• Example: (3,4) means go 3 right and 4 up. • The point (0,0) is referred to as the origin
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Quadrants
• The intersecting lines break the coordinate plane into four Quadrants.
• These regions allow us to locate on a coordinate plane where certain points are located
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Y-axis
X-axis
Quadrant 1 (+,+)
Quadrant 2(-,+)
Quadrant 3(-,-)
Quadrant 4(+,-) Origin (0,0)
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Graph Ordered Pairs
A. Graph the ordered pair (3, 4) on a coordinate plane.
Step 1 Start at the origin.Step 2 Since the x-coordinate
is 3, move 3 units to the right.
Step 3 Since the y-coordinate is 4, move 4 units up. Draw a dot.
Answer:
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Graph Ordered Pairs
B. Graph the ordered pair (0, 2) on a coordinate plane.
Step 1 Start at the origin.Step 2 Since the x-coordinate
is 0, you will not need to move to the right.
Step 3 Since the y-coordinate is 2, move 2 units up. Draw a dot.
Answer:
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A. A
B. B
C. C
D. D
A. Graph the ordered pair (2, 5) on a coordinate plane.
A. B.
C. D. none of the above
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A. A
B. B
C. C
D. D
B. Graph the ordered pair (4, 0) on a coordinate plane.
A. B.
C. D. none of the above
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Identify Ordered Pairs
Step 1 Start at the origin.
A. Write the ordered pair that names point G.
Answer: The ordered pair for G is (1, 1).
Step 2 Move right on the x-axis to find the x-coordinate of point G, which is 1.
Step 3 Move up the y-axis to find the y-coordinate, which is 1.
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Identify Ordered Pairs
B. Write the ordered pair that names point H.
Step 1 Start at the origin.
Answer: The ordered pair for H is (4, 0).
Step 2 Move right on the x-axis to find the x-coordinate of point H, which is 4.
Step 3 Since the y-coordinate is zero, you will not need to move up.
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A. A
B. B
C. C
D. D
A. (2, 5)
B. (3, 5)
C. (2, 3)
D. (3, 2)
A. Write the ordered pair that names point A.
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A. A
B. B
C. C
D. D
A. (6, 6)
B. (0, 6)
C. (0, 0)
D. (6, 0)
B. Write the ordered pair that names point B.
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• Domain is the collection of all the x-values in a relation or a graph
• Range is the collection of all the y-values in a relation or a graph
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Relations as Tables
Express the relation {(1, 4), (2, 2), (3, 0), (0, 2)} as a table. Then determine the domain and range.
Answer:
The domain is {0,1, 2, 3}.
The range is {0, 2, 4}.
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A. A
B. B
C. C
D. D
Express the relation {(4, 1), (3, 2), (0, 1), (2, 3)} as a table. Then determine the domain and range.
A. D = {1, 2, 3}, R = {0, 2, 3, 4}
B. D = {0, 2, 3, 4}, R = {1, 2, 3}
C. D = {2, 3, 4}, R = {1, 2, 3}
D. D = {1, 2, 3}, R = {2, 3, 4}
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Relations as Graphs
EARNINGS José earns $5 an hour doing yard work.
A. Make a table of ordered pairs in which the x-coordinate represents the hours worked and the y-coordinate represents the amount of money José earns for 1, 2, 3, and 5 hours of work.
Answer:
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Relations as Graphs
EARNINGS José earns $5 an hour doing yard work.
B. Graph the ordered pairs and describe the graph.
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Relations as Graphs
Answer: The points appear to lie on a line.