review for 3rd 9 weeks test

Transcription

1 Class: Date: review for 3rd 9 weeks test What are the variables in each graph? Describe how the variables are related at various points on the graph. 1. Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are at traffic lights and the homes where she makes the deliveries. The graph shows her distance from the store on her first trip for the day. What are the variables? Describe how the variables are related at various points on the graph. 2. The graph shows the number of handbags that Mandy made in one day. What are the variables? Describe how the variables are related at various points on the graph. 1

2 In the diagram below, what is the relationship between the number of rectangles and the perimeter of the figure they form? 3. Represent the relationship above using words. What is an equation for this relationship? In the diagram below, what is the relationship between the number of triangles and the perimeter of the figure they form? 4. Represent the above relationship by filling in the table below. Number of Triangles 1 Perimeter 2 3 2

3 5. Represent the above relationship by drawing a graph. 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) Describe the above relationship using words. What is the equation for this relationship? The table shows the total number of squares in each figure below. What is a pattern you can use to complete the table? 7. What is a pattern you can use to complete the table? Represent the relationship using words. 3

4 8. Model the function rule y = 1 x + 3 with a table of values and a graph. 6 x 1 y 0 1 4

5 9. Model the function rule y = 5x 13 with a table of values and a graph. x 1 y 0 1 5

6 10. Elaine has a business repairing home computers. She charges a base fee of $30 for each visit and $35 per hour for her labor. The total cost C for a home visit and x hours of labor is modeled by the function rule C = 35x Use the function rule to make a table of values and a graph. x C 11. Fahrenheit and Celsius are two measures of temperature. The temperature in degrees Celsius is equal to five ninths of 32 less than the temperature in degrees Fahrenheit. What is a function rule that represents this situation? 12. An employee receives a weekly salary of $340 and a 6% commission on all sales. a. Write a rule to describe the function f(d) that gives weekly earnings in terms of d dollars in sales. b. Find the employee s earnings for a week with $660 total sales. c. What were the employee s total sales for a week in which her earnings were $1300? 13. Write a function rule for the area of a parallelogram whose base is 4 inches more than its height. What is the area of the parallelogram when its height is 8 inches? 14. Identify the domain and range of the relation. ÏÔ Ì( 9, 2), ( 4, 2), (3, 2), (9, 2) Ô ÓÔ Ô 6

7 15. Identify the domain and range of the relation. ÏÔ Ì( 4, 2), ( 9, 5), ( 4, 12), (8, 8) Ô ÓÔ Ô Use the vertical line test to determine whether the relation is a function. 16. Ï 17. Ô Ì(0, 1), ( 5, 1), ( 3, 3), ( 5, 5) Ô ÓÔ Ô 18. Ï 19. Ô Ì(3, 0), (2, 1), ( 1, 4), (1, 2) Ô ÓÔ Ô 7

8 20. The function g(t) = 2t represents the number of guitar lessons, g(t), you can complete in t months. How many guitar lessons can you complete in 7 months? 21. Find the range of f( x) = 2x + 6 for the domain { 1, 3, 7, 9}. 22. Find the range of f( x) = 2 x + 5 for the domain { 4, 2, 0, 3} Find the range of f( x) = 4.7x + 1 for the domain { 1, 3, 5, 8}. 24. Dexter has 83 tiles left over from tiling his bathroom floor and he would like to use them to tile the front entrance of his house. Each tile has an area of 49 in. 2. The function A(t) = 49t represents the area A(t), in square inches, that t tiles cover. What domain and range are reasonable for the function? What is the graph of the function? 25. The cost to ride the city bus is $2.00 one way. Next year, the cost will be $2.10 one way. The year after that the cost will be $2.20 one way, and after that the fare will be $2.30. Write a rule to represent the cost of riding the city bus one way as an arithmetic sequence. How much will it cost to ride the bus 12 years from now? What equation in slope intercept form represents the line that passes through the two points? 26. (2, 5), (9, 2) A. y = 3 7 x 41 7 B. y = 7 3 x 41 7 C. y = 7 3 x D. y = 3 7 x

9 Graph the equation. 27. y = 4x 3 A. B. C. D. Write an equation in point-slope form for the line through the given point with the given slope. 28. (8, 3); m = 6 A. y + 3 = 6(x 8) B. y 3 = 6(x 8) C. y 3 = 6(x + 8) D. y + 3 = 6x + 8 9

10 What is an equation of the line? 29. A. y 4 = 1 2 (x + 2) B. y 2 = 3 8 (x + 4) C. y 1 = 3 8 (x + 4) D. y 2 = 8 (x + 4) A. y 2 = 4.5(x + 3) B. y 2 = 4.5(x + 3) C. y 2.5 = 0.2(x + 3) D. y 2.5 = 0.2(x 2) 10

11 31. The table shows the height above the ground of a helicopter taking off from the top of a building. What equation in point-slope form gives the helicopter s height at any time? Let y stand for the height of the helicopter in m and let x stand for the time in seconds. Time (s) Height (m) A. y 21 = 7(x 3) B. y 3 = 7 2 (x 21) C. y 21 = 7 (x 3) D. The relationship cannot be modeled. 2 Find the x- and y-intercept of the line. 32. x 6y = 12 A. x-intercept is 12; y-intercept is 2 B. x-intercept is 6; y-intercept is 1 C. x-intercept is 2; y-intercept is 12 D. x-intercept is 1; y-intercept is 6 11

12 Match the equation with its graph x 5y = 40 A. B. C. D. 12

13 review for 3rd 9 weeks test Answer Section 1. ANS: The variables are distance and time. The distance from the store increases as she drives, and it stays constant each time she stops for a traffic light or to stop at a customer s house. After her third stop, she starts heading back to the store. The distance from the store decreases as she drives, and it stays constant for one more stop. Finally, she makes it back to the store and the distance is zero again. 2. ANS: The variables are the number of handbags and time. The flat parts of the graph show either where Mandy is working on a handbag or taking a break. As soon as Mandy finishes a bag, the graph jumps up a level to show that she has completed one more bag. 3. ANS: Multiply twice the width of one rectangle by the number of rectangles in each figure to get the total length of the top and bottom sides of the combined figure. Then add 2(8), or 16, for the total length of the left and right sides of the combined figure to get the entire perimeter. An equation for this situation is y = 10x + 16, where x is the number of rectangles and y is the perimeter of the combined figure. STA: MA.912.A.2.3 MA.912.A ANS: Number of Triangles Perimeter STA: MA.912.A.2.3 MA.912.A.3.8 1

14 5. ANS: STA: MA.912.A.2.3 MA.912.A ANS: For every sports team the person joins, he or she spends 7 hours per week practicing. So, the amount of free time the person has, F, is the amount of free time they would have if they did not belong to any sports teams minus 7 times the number of teams they belong to. In equation form this is F = 46 7n. STA: MA.912.A.2.3 MA.912.A ANS: The number of squares in each figure, y, is equal to the xth odd number squared plus 4. STA: MA.912.A.2.3 MA.912.A

15 8. ANS: x 1 y STA: MA.912.A.2.3 MA.912.A.2.13 MA.912.A.3.8 3

16 9. ANS: x y STA: MA.912.A.2.3 MA.912.A.2.13 MA.912.A.3.8 4

17 10. ANS: x C STA: MA.912.A.2.3 MA.912.A.2.13 MA.912.A ANS: C = 5 (F 32) 9 STA: MA.912.A.2.3 MA.912.A ANS: a. f(d) = d b. $ c. $16,000 STA: MA.912.A.2.3 MA.912.A ANS: Let h stand for the height of the parallelogram and let A(h) stand for the area. The function rule is A(h) = h 2 + 4h. When the height is 8 inches, the area of the parallelogram is 96 square inches. STA: MA.912.A.2.3 MA.912.A ANS: The domain is { 9, 4, 3, 9}. The range is {2}. 5

18 15. ANS: The domain is { 9, 4, 8}. The range is { 8, 5, 2, 12}. 16. ANS: The relation is a function. 17. ANS: The relation is not a function. 18. ANS: The relation is not a function. 19. ANS: The relation is a function. 20. ANS: You can complete 14 guitar lessons in 7 months. 21. ANS: {8, 0, 8, 12} 22. ANS: { 17 5, 21 31,5, 5 5 } 23. ANS: {5.7, 13.1, 22.5, 36.6} 6

19 24. ANS: The domain is 0 t 83. The range is 0 A(t) ANS: A(n) = (n 1)0.10 In 12 years it will cost $3.10 to ride the bus one way. 26. ANS: D STA: MA.912.A.3.7 MA.912.A.3.8 MA.912.A.3.9 MA.912.A.3.10 MA.912.A.3.12 MA.912.G ANS: D STA: MA.912.A.3.7 MA.912.A.3.8 MA.912.A.3.9 MA.912.A.3.10 MA.912.A.3.12 MA.912.G ANS: B STA: MA.912.A.3.8 MA.912.A.3.9 MA.912.A.3.10 MA.912.A.3.11 MA.912.A.3.12 MA.912.G ANS: B STA: MA.912.A.3.8 MA.912.A.3.9 MA.912.A.3.10 MA.912.A.3.11 MA.912.A.3.12 MA.912.G ANS: A STA: MA.912.A.3.8 MA.912.A.3.9 MA.912.A.3.10 MA.912.A.3.11 MA.912.A.3.12 MA.912.G ANS: A STA: MA.912.A.3.8 MA.912.A.3.9 MA.912.A.3.10 MA.912.A.3.11 MA.912.A.3.12 MA.912.G ANS: A STA: MA.912.A.3.7 MA.912.A.3.8 MA.912.A.3.9 MA.912.A ANS: C STA: MA.912.A.3.7 MA.912.A.3.8 MA.912.A.3.9 MA.912.A