Algebra Chapter 4 (pearson) review

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1 Class: Date: Algebra Chapter 4 (pearson) review What are the variables in each graph? Describe how the variables are related at various points on the graph. 1. The graph shows the height of a hiker above sea level. The hiker walks at a constant speed for the entire trip. What are the variables? Describe how the variables are related at various points on the graph. a. The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is climbing a steep incline. Flat parts of the graph show where the elevation does not change, which means the hiker stopped to rest. The steep part at the end of the graph shows that the hiker is descending a gentle slope. b. The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is walking up a gentle slope. Flat parts of the graph show where the elevation does not change, which means the trail is flat here. The steep part at the end of the graph shows that the hiker is descending a steep incline. c. The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is climbing a steep incline. Flat parts of the graph show where the elevation does not change, which means the trail is flat here. The steep part at the end of the graph shows that the hiker is descending a steep incline. d. All of the above. 1

2 2. The table shows the amount of money made by a summer blockbuster in each of the first four weeks of its theater release. Which graph could represent the data shown in the table? Week Money ($) 1 26,600, ,900, ,600, ,700,000 2

3 3. A hiker climbs up a steep bank and then rests for a minute. He then walks up a small hill and finally across a flat plateau. What sketch of a graph could represent the elevation of the hiker? Any of the graphs could represent the situation, depending on the hiker s speed. 3

4 In the diagram below, what is the relationship between the number of rectangles and the perimeter of the figure they form? 4. Which of the following tables represent the relationship in the diagram above? 4

5 5. Which of the following graphs represents the relationship described above? The table shows the relationship between the number of sports teams a person belongs to and the amount of free time the person has per week. Number of Sports Teams Free Time (hours) Is the above relationship a linear function? a. yes b. no 5

6 7. What is the graph for the above relationship? 8. The ordered pairs (1, 1), (2, 8), (3, 27), (4, 64), and (5, 125) represent a function. What is a rule that represents this function? a. y = 3x c. y = 3 x b. y = x + 3 d. y = x 3 9. The ordered pairs (1, 49), (2, 64), (3, 81), (4, 100), and (5, 121) represent a function. What is a rule that represents this function? a. y = 6 x c. y = x 6 b. y = 6x d. y = (x + 6) 2 6

7 What is the graph of the function rule? 10. y = 4x + 1 7

8 11. A taxi company charges passengers $1.00 for a ride, and an additional $0.25 for each mile traveled. The function rule C = 0.25m describes the relationship between the number of miles m and the total cost of the ride c. If the taxi company will only go a maximum of 40 miles, what is a reasonable graph of the function rule? Write a function for the situation. Is the graph continuous or discrete? 12. A movie store sells DVDs for $20 each. What is the cost, C, of n DVDs? a. C = 20n; discrete c. C = 20 + n; continuous b. C = 20n; continuous d. C = 20 + n; discrete 13. A produce stand sells roasted peanuts for $2.60 per pound. What is the cost, C, of p pounds of peanuts? a. C = 2.60p; continuous c. C = 2.60p; discrete b. C = p; discrete d. C = p; continuous 8

9 What is the graph of each function rule? 14. y = x 3 9

10 15. y = 2x

11 16. y = x

12 17. y = 2x Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $.30. a. c(p) = 0.30p c. c(p) = p b. c(p) = p 0.30 d. c(p) = 30p 19. A snail travels at a rate of 2.14 feet per minute. Write a rule to describe the function. How far will the snail travel in 7 minutes? a. d(t) = 7t; ft c. d(t) = t ; 9.14 ft t b. d(t) = 2.14t; ft d. d(t) = ; 3.27 ft

13 20. Crystal earns $5.50 per hour mowing lawns. Write a rule to describe how the amount of money m earned is a function of the number of hours h spent mowing lawns. How much does Crystal earn if she works 1 hour and 45 minutes? h a. m(h) = ; $0.32 c. m(h) = h + 45; $ b. m(h) = 5.50h; $9.63 d. m(h) = 5.50h; $ A zucchini plant in Darnell s garden was 9 centimeters tall when it was first planted. Since then, it has grown approximately 0.7 centimeter per day. Write a rule to describe the function. After how many days will the zucchini plant be meter tall? a. h(d) = 0.7d; 26 days c. h(d) = d + 9; 6 days 0.7 b. h(d) = 0.7d + 9; 13 days d. h(d) = 9d + 0.7; 1.3 days 22. Identify the mapping diagram that represents the relation and determine whether the relation is a function. Ï Ô Ô Ì ( 8, 6), ( 5, 2), ( 8, 1), (7, 3) Ô Ô Ô Ó Ô a. c. b. The relation is a function. d. The relation is not a function The relation is a function. The relation is not a function. 13

14 23. The function j(x) = 43x represents the number of jumping jacks j(x) you can do in x minutes. How many jumping jacks can you do in 20 minutes? a. 223 jumping jacks c. 163 jumping jacks b. 860 jumping jacks d. 2 jumping jacks 24. The function b(n) = 9n represents the number of light bulbs b(n) that are needed for n chandeliers. How many light bulbs are needed for 17 chandeliers? a. 153 light bulbs c. 152 light bulbs b. 158 light bulbs d. 1 light bulbs Describe a pattern in each sequence. What are the next two terms of each sequence? , 26, 23, 20,... a. add 3 to the previous term; 23, 26 b. subtract 3 from the previous term; 17, 14 c. multiply the previous term by 3; 17, 180 d. multiply the previous term by 3; 60, , 6, 12, 24,... a. subtract 3 from the previous term; 48, 96 b. add 3 to the previous term; 21, 18 c. multiply the previous term by 2; 48, 96 d. multiply the previous term by 2; 48, , 3, 9, 27,... a. multiply the previous term by 3; 81, 243 b. add 4 to the previous term; 23, 19 c. multiply the previous term by 3; 81, 243 d. subtract 4 from the previous term; 81, 243 Tell whether the sequence is arithmetic. If it is, what is the common difference? , 13, 9, 5,... a. yes; 4 b. yes; 30 c. yes; d. no 29. 3, 7, 12, 18,... a. yes; 4 b. yes; 5 c. yes; 3 d. no 14

15 The table shows the total number of squares in each figure below. What is a pattern you can use to complete the table? 30. Which of the following equations represents the pattern above? a. y = (2x + 4) 2 c. y = (2x) b. y = (2x + 1) d. y = (2x 1)

16 Algebra Chapter 4 (pearson) review Answer Section 1. ANS: B PTS: 1 DIF: L3 REF: 4-1 Using Graphs to Relate Two Quantities OBJ: To represent mathematical relationships using graphs NAT: CC F.IF.4 TOP: 4-1 Problem 1 Analyzing a Graph KEY: interpreting a graph 2. ANS: D PTS: 1 DIF: L3 REF: 4-1 Using Graphs to Relate Two Quantities OBJ: To represent mathematical relationships using graphs NAT: CC F.IF.4 TOP: 4-1 Problem 2 Matching a Table and a Graph KEY: sketching a graph modeling a relationship 3. ANS: A PTS: 1 DIF: L3 REF: 4-1 Using Graphs to Relate Two Quantities OBJ: To represent mathematical relationships using graphs NAT: CC F.IF.4 TOP: 4-1 Problem 3 Sketching a Graph KEY: sketching a graph modeling a relationship 4. ANS: A PTS: 1 DIF: L3 REF: 4-2 Patterns and Linear Functions OBJ: To identify and represent patterns that describe linear functions NAT: CC A.REI.10 CC F.IF.4 A.1.a A.1.b A.1.e A.1.h TOP: 4-2 Problem 1 Representing a Geometric Relationship KEY: dependent variable independent variable function linear function modeling a relationship 5. ANS: B PTS: 1 DIF: L3 REF: 4-2 Patterns and Linear Functions OBJ: To identify and represent patterns that describe linear functions NAT: CC A.REI.10 CC F.IF.4 A.1.a A.1.b A.1.e A.1.h TOP: 4-2 Problem 1 Representing a Geometric Relationship KEY: dependent variable independent variable function linear function sketching a graph modeling a relationship 6. ANS: A PTS: 1 DIF: L3 REF: 4-2 Patterns and Linear Functions OBJ: To identify and represent patterns that describe linear functions NAT: CC A.REI.10 CC F.IF.4 A.1.a A.1.b A.1.e A.1.h TOP: 4-2 Problem 2 Representing a Linear Function KEY: dependent variable independent variable function linear function create equations in two variables 7. ANS: A PTS: 1 DIF: L3 REF: 4-2 Patterns and Linear Functions OBJ: To identify and represent patterns that describe linear functions NAT: CC A.REI.10 CC F.IF.4 A.1.a A.1.b A.1.e A.1.h TOP: 4-2 Problem 2 Representing a Linear Function KEY: dependent variable independent variable function linear function sketching a graph modeling a relationship 8. ANS: D PTS: 1 DIF: L3 REF: 4-3 Patterns and Nonlinear Functions OBJ: To identify and represent patterns that describe nonlinear functions NAT: CC A.REI.10 CC F.IF.4 A.1.a A.1.e TOP: 4-3 Problem 3 Writing a Rule to Describe a Nonlinear Function KEY: nonlinear function 1

17 9. ANS: D PTS: 1 DIF: L4 REF: 4-3 Patterns and Nonlinear Functions OBJ: To identify and represent patterns that describe nonlinear functions NAT: CC A.REI.10 CC F.IF.4 A.1.a A.1.e TOP: 4-3 Problem 3 Writing a Rule to Describe a Nonlinear Function KEY: nonlinear function 10. ANS: A PTS: 1 DIF: L2 REF: 4-4 Graphing a Function Rule OBJ: To graph equations that represent functions NAT: CC N.Q.1 CC A.REI.10 CC F.IF.5 A.1.b TOP: 4-4 Problem 1 Graphing a Function Rule KEY: continuous graph 11. ANS: A PTS: 1 DIF: L3 REF: 4-4 Graphing a Function Rule OBJ: To graph equations that represent functions NAT: CC N.Q.1 CC A.REI.10 CC F.IF.5 A.1.b TOP: 4-4 Problem 2 Graphing a Real-World Function Rule KEY: continuous graph choosing the correct scale 12. ANS: A PTS: 1 DIF: L3 REF: 4-4 Graphing a Function Rule OBJ: To graph equations that represent functions NAT: CC N.Q.1 CC A.REI.10 CC F.IF.5 A.1.b TOP: 4-4 Problem 3 Identifying Continuous and Discrete Graphs KEY: continuous graph discrete graph 13. ANS: A PTS: 1 DIF: L3 REF: 4-4 Graphing a Function Rule OBJ: To graph equations that represent functions NAT: CC N.Q.1 CC A.REI.10 CC F.IF.5 A.1.b TOP: 4-4 Problem 3 Identifying Continuous and Discrete Graphs KEY: continuous graph discrete graph 14. ANS: B PTS: 1 DIF: L2 REF: 4-4 Graphing a Function Rule OBJ: To graph equations that represent functions NAT: CC N.Q.1 CC A.REI.10 CC F.IF.5 A.1.b TOP: 4-4 Problem 4 Graphing Nonlinear Function Rules KEY: continuous graph 15. ANS: A PTS: 1 DIF: L3 REF: 4-4 Graphing a Function Rule OBJ: To graph equations that represent functions NAT: CC N.Q.1 CC A.REI.10 CC F.IF.5 A.1.b TOP: 4-4 Problem 4 Graphing Nonlinear Function Rules KEY: continuous graph 16. ANS: A PTS: 1 DIF: L2 REF: 4-4 Graphing a Function Rule OBJ: To graph equations that represent functions NAT: CC N.Q.1 CC A.REI.10 CC F.IF.5 A.1.b TOP: 4-4 Problem 4 Graphing Nonlinear Function Rules KEY: continuous graph 17. ANS: A PTS: 1 DIF: L3 REF: 4-4 Graphing a Function Rule OBJ: To graph equations that represent functions NAT: CC N.Q.1 CC A.REI.10 CC F.IF.5 A.1.b TOP: 4-4 Problem 4 Graphing Nonlinear Function Rules KEY: continuous graph 18. ANS: A PTS: 1 DIF: L3 REF: 4-5 Writing a Function Rule OBJ: To write equations that represent functions NAT: CC N.Q.2 CC A.SSE.1.a CC A.CED.2 A.1.b TOP: 4-5 Problem 1 Writing a Function Rule KEY: create equations in two variables 2

18 19. ANS: B PTS: 1 DIF: L2 REF: 4-5 Writing a Function Rule OBJ: To write equations that represent functions NAT: CC N.Q.2 CC A.SSE.1.a CC A.CED.2 A.1.b TOP: 4-5 Problem 2 Writing and Evaluating a Function Rule KEY: create equations in two variables 20. ANS: B PTS: 1 DIF: L3 REF: 4-5 Writing a Function Rule OBJ: To write equations that represent functions NAT: CC N.Q.2 CC A.SSE.1.a CC A.CED.2 A.1.b TOP: 4-5 Problem 2 Writing and Evaluating a Function Rule KEY: create equations in two variables 21. ANS: B PTS: 1 DIF: L4 REF: 4-5 Writing a Function Rule OBJ: To write equations that represent functions NAT: CC N.Q.2 CC A.SSE.1.a CC A.CED.2 A.1.b TOP: 4-5 Problem 2 Writing and Evaluating a Function Rule KEY: create equations in two variables 22. ANS: D PTS: 1 DIF: L3 REF: 4-6 Formalizing Relations and Functions OBJ: To determine whether a relation is a function NAT: CC F.IF.1 CC F.IF.2 N.2.c A.1.b A.1.g A.1.i A.3.f TOP: 4-6 Problem 1 Identifying Functions Using Mapping Diagrams KEY: relation domain range 23. ANS: B PTS: 1 DIF: L2 REF: 4-6 Formalizing Relations and Functions OBJ: To find domain and range and use function notation NAT: CC F.IF.1 CC F.IF.2 N.2.c A.1.b A.1.g A.1.i A.3.f TOP: 4-6 Problem 3 Evaluating a Function KEY: function notation 24. ANS: A PTS: 1 DIF: L2 REF: 4-6 Formalizing Relations and Functions OBJ: To find domain and range and use function notation NAT: CC F.IF.1 CC F.IF.2 N.2.c A.1.b A.1.g A.1.i A.3.f TOP: 4-6 Problem 3 Evaluating a Function KEY: function notation 25. ANS: B PTS: 1 DIF: L3 REF: 4-7 Sequences and Functions OBJ: To identify and extend patterns in sequences NAT: CC A.SSE.1.a CC A.SSE.1.b CC F.LE.2 CC F.IF.3 CC F.BF.1.a CC F.BF.2 CC F.IF.6 CC F.LE.1.b A.1.b TOP: 4-7 Problem 1 Extending Sequences KEY: sequence term of a sequence arithmetic sequence 26. ANS: D PTS: 1 DIF: L3 REF: 4-7 Sequences and Functions OBJ: To identify and extend patterns in sequences NAT: CC A.SSE.1.a CC A.SSE.1.b CC F.LE.2 CC F.IF.3 CC F.BF.1.a CC F.BF.2 CC F.IF.6 CC F.LE.1.b A.1.b TOP: 4-7 Problem 1 Extending Sequences KEY: sequence term of a sequence arithmetic sequence 27. ANS: C PTS: 1 DIF: L3 REF: 4-7 Sequences and Functions OBJ: To identify and extend patterns in sequences NAT: CC A.SSE.1.a CC A.SSE.1.b CC F.LE.2 CC F.IF.3 CC F.BF.1.a CC F.BF.2 CC F.IF.6 CC F.LE.1.b A.1.b TOP: 4-7 Problem 1 Extending Sequences KEY: sequence term of a sequence arithmetic sequence 28. ANS: A PTS: 1 DIF: L2 REF: 4-7 Sequences and Functions OBJ: To identify and extend patterns in sequences NAT: CC A.SSE.1.a CC A.SSE.1.b CC F.LE.2 CC F.IF.3 CC F.BF.1.a CC F.BF.2 CC F.IF.6 CC F.LE.1.b A.1.b TOP: 4-7 Problem 2 Identifying an Arithmetic Sequence KEY: sequence arithmetic sequence common difference 3

19 29. ANS: D PTS: 1 DIF: L3 REF: 4-7 Sequences and Functions OBJ: To identify and extend patterns in sequences NAT: CC A.SSE.1.a CC A.SSE.1.b CC F.LE.2 CC F.IF.3 CC F.BF.1.a CC F.BF.2 CC F.IF.6 CC F.LE.1.b A.1.b TOP: 4-7 Problem 2 Identifying an Arithmetic Sequence KEY: sequence arithmetic sequence common difference 30. ANS: D PTS: 1 DIF: L3 REF: 4-3 Patterns and Nonlinear Functions OBJ: To identify and represent patterns that describe nonlinear functions NAT: CC A.REI.10 CC F.IF.4 A.1.a A.1.e TOP: 4-3 Problem 2 Representing Patterns and Nonlinear Functions KEY: nonlinear function 4