1-6 Ordered Pairs and Relations

Transcription

1 Graph each ordered pair on a coordinate plane. 2. A(2, 5) Start at the origin. The x-coordinate is 2, so move 2 units to the right. The y-coordinate is 5, so move 5 units up. Draw a dot, and label it A. 4. Z(0, 1) Start at the origin. The x-coordinate is 0, so you do not need to move to the right. The y-coordinate is 1, so move 1 unit up. Draw a dot, and label it Z. esolutions Manual - Powered by Cognero Page 1

2 Refer to the coordinate plane shown below. Write the ordered pair that names each point. 6. K Start at the origin. Move right on the x-axis to find the x-coordinate of point K, which is 2. Move up the y-axis to find the y-coordinate, which is 1. The ordered pair for point K is (2, 1). 8. M Start at the origin. Move right on the x-axis to find the x-coordinate of point M, which is 6. Move up the y-axis to find the y-coordinate, which is 6. The ordered pair for point M is (6, 6). Express each relation as a table. Then determine the domain and range. 10. {(1, 3), (2, 6), (3, 3), (4, 7)} x y The domain is {1, 2, 3, 4} and the range is {3, 6, 7}. esolutions Manual - Powered by Cognero Page 2

3 Graph each ordered pair on a coordinate plane. 12. A(4, 7) Start at the origin. The x-coordinate is 4, so move 4 units to the right. The y-coordinate is 7, so move 7 units up. Draw a dot, and label it A. 14. C(7, 3) Start at the origin. The x-coordinate is 7, so move 7 units to the right. The y-coordinate is 3, so move 3 units up. Draw a dot, and label it C. esolutions Manual - Powered by Cognero Page 3

4 16. F(6, 1) Start at the origin. The x-coordinate is 6, so move 6 units to the right. The y-coordinate is 1, so move 1 unit up. Draw a dot, and label it F. 18. H(3, 0) Start at the origin. The x-coordinate is 3, so move 3 units to the right. The y-coordinate is 0, so you do not need to move up. Draw a dot, and label it H. Refer to the coordinate system shown below. Write the ordered pair that names each point. 20. L The x-coordinate of point L is 2, and the y-coordinate is 4. The ordered pair for point L is (2, 4). esolutions Manual - Powered by Cognero Page 4

5 22. N 24. Q 26. S The x-coordinate of point N is 2, and the y-coordinate is 1. The ordered pair for point N is (2, 1). The x-coordinate of point Q is 3, and the y-coordinate is 7. The ordered pair for point Q is (3, 7). The x-coordinate of point S is 5, and the y-coordinate is 0. The ordered pair for point S is (5, 0). Express each relation as a table. Then determine the domain and range. 28. {(4, 5), (2, 1), (5, 0), (3, 2)} x y The domain is {2, 3, 4, 5} and the range is {0, 1, 2, 5}. 30. {(6, 0), (4, 5), (2, 1), (3, 1)} x y The domain is {2, 3, 4, 6} and the range is {0, 1, 5}. esolutions Manual - Powered by Cognero Page 5

6 32. The cost of a mini pizza is $7 at Pizza Pizza. a. Make a table of ordered pairs in which the x-coordinate represents the number of mini pizzas and the y-coordinate represents the cost of 1, 3, 5, and 7 mini pizzas at Pizza Pizza. b. Graph the ordered pairs. Then describe the graph. a. 1 pizza costs $7 x (Number y (Cost, $) (x, y) of Pizzas) = 7 (1, 7) = 21 (3, 21) = 35 (5, 35) = 49 (7, 49) b. The number of pizzas is graphed along the x-axis. The cost is graphed along the y-axis. The points appear to lie in a line that slants up from left to right. 34. Multiple Representations In this problem, you will explore more about relations. Suppose Jamal has only 30 minutes to practice the piano and study for a science test. a. Table Make a table of ordered pairs showing at least 6 ways Jamal can split the time between the two activities. Let the x-coordinate represent the number of minutes spent playing the piano and the y-coordinate represent the number of minutes spent studying, respectively. b. Graph Graph the ordered pairs. c. Words Describe the general pattern of points of your graph. d. Graph Choose a point on the graph that is not one of the points you plotted. Use the coordinates to predict a pair of values for the piano time and study time. a. Find six pairs of numbers that have a sum of 30. x y (x, y) (Piano Time, min) (Study Time, min) = 25 (5, 25) = 20 (10, 20) = 15 (15, 15) esolutions Manual - Powered by Cognero Page 6

7 = 10 (20, 10) = 5 (25, 5) = 0 (30, 0) b. Jamal s piano time is graphed along the x-axis. His study time is graphed along the y-axis. c. The points appear to lie in a straight line that slants down from left to right. d. Sample answer: (12, 18): If Jamal spends12 minutes playing the piano, he will have 18 minutes left to study for the test. esolutions Manual - Powered by Cognero Page 7

8 36. Multiple Representations The numbers 4, 7, 10, 13, form an arithmetic sequence because each term can be found by adding the same number to the previous term. a. Numbers Write the set of ordered pairs (term number, term). b. Graph Graph the ordered pairs. c. Words Describe the shape of the graph. d. Words If possible, write a rule to find the twentieth term. Explain how you found the rule or why you cannot write a rule. a. The set of ordered pairs is {(1, 4), (2, 7), (3, 10), (4, 13)}. b. c. The points appear to lie in a straight line that slants up and to the right. The graph shows a positive, linear relationship. d. Term Number Term = 4 1 = 7 1 = 10 1 = 13 Multiplying the term number by 3 and adding 1 gives the term. So, you would multiply 3 times the x value plus 1 equals the y-value. The twentieth term would be or Persevere with Problems Describe all of the possible locations for the graph of (x, y) if x = 2. x = 2 at every point that is 2 units to the right of the y-axis. So, the graph of (x, y) where x = 2 is the vertical line x = 2. esolutions Manual - Powered by Cognero Page 8

9 40. Building on the Essential Question Explain why the point M(4, 3) is different from the point N(3, 4). Sample answer: Point M is 4 units to the right on the x-axis and 3 units up the y-axis. Point N is 3 units to the right on the x-axis and 4 units up the y-axis. 42. Rectangle ABCD has vertices A(1, 3), B(1, 6), and C(5, 6). What are the coordinates of point D? F (6, 5) G (5, 1) H (5, 3) J (6, 1) For the points to make a rectangle, the coordinates of point D would be (5, 3). Choice H is correct. 44. Short Response Point Z is located at (4, 7) on a coordinate plane. Point T is located 3 units to the right and 4 units down from point Z. What is the x-coordinate of point T? The x-coordinate of Point Z is 4. If Point T is 3 units to the right of Point Z, then the x-coordinate of Point T is or 7. Name the property shown by each statement = 0 When any number is multiplied by 0, the product is 0. This is the Multiplicative Property of Zero. esolutions Manual - Powered by Cognero Page 9

10 48. (5 + x) + 6 = 5 + (x + 6) The grouping of the numbers changed. This is the Associative Property of Addition. State whether each conjecture is true. If not, give a counterexample. 50. Subtraction of whole numbers is commutative. 9 3 = = and therefore No, subtraction of whole numbers is not commutative. Find the value of each expression. 52. x + 7 if x = m if m = s + 14 if s = 32 Find the value of each expression esolutions Manual - Powered by Cognero Page 10

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