8 th Grade Domain 2: Algebra and Functions (40%) Sara

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1 8 th Grade Domain 2: Algebra and Functions (40%) 1. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times. Find the slope of the line and tell what the slope represents in this specific scenario. MGSE8.EE.5 50; gain fifty dollars each week. 50 ; decrease by fifty dollars each week. 1/50; gain fifty dollars each week. 1/50; decrease by fifty dollars each week. 2. The table shows the relationship between the number of hours, h, John has been hiking and the total distance, d, he has traveled in kilometers. The graph shows the distance Sara hiked over the same time period. Who hikes faster? MGSE8.EE.5 Sara John They hike at the same rate There is not enough information to determine 3. Three students saved money for four weeks. Antwan made a graph to show how much money he saved. Carla made a table to show how much money she saved. Omar wrote an equation to show how much he saved. In the equation, S is the total amount of money saved, in dollars, and w is the number of weeks. Write the 3 students names in order from least to greatest according to the rate of change of their functions. MGSE8.EE.5 Antwan, Carla, Omar Carla, Antwan, Omar Carla, Omar Antwan Omar, Carla, Antwan Antwan Omar Amount ($) S 2. 5w (4, 2400) (12, 2000) Time (weeks) John Sara Carla

2 4. Julio is training for a swimming race. The first part of his training schedule is shown. Is this training schedule a linear function? Explain why or why not. MGSE8.EE.5 No, it s not linear. The rate is change is constant. Yes, it s linear. The rate of change is constant. Session Swimming distance (mi) Yes, it s linear. The rate is change is not constant No, it s not linear. The rate of change is not constant. 5. According to the table in number 11, how many miles will Julio swim on the 14 th day? MGSE8.EE miles 3.55 miles 3.85 miles 4.15 miles 6. The rate of change for the function is constant. Calculate the slope. MGSE8.EE Amounts ($) Resale Value of a Refrigerator Years after original purchase

3 7. The graph to the right depicts the travel time in hours and the distance that Jerome traveled to Tennessee. Is this a proportional relationship? What is the rate of change? MGSE8.EE.5 Yes, proportional. The rate of change is 60 mph. No, not proportional. The rate of change is 60 mph. Yes, proportional. The rate of change is 40 mph. No, not proportional. The rate of change is 40 mph. 8. Which graph is represented by the equation 1 y x 3? MGSE8.EE Which equation below represents the graph to the right? MGSE8.EE.6 3 y x y x 4 3 y 4x 3 y 3x 4

4 10. What is the equation of the line to the right written in slope intercept form? MGSE8.EE.6 y y y y 1 5 x x x 5 2 4x Which graph is represented by the equation 5 y x 3 MGSE8.EE If a line contains the points in the table to the right, what is the equation of the line? MGSE8.EE.6 y 2x 5 y 2x 5 y 5x 2 y 5x 2

5 13. Mr. Perry s students used pairs of points to find the slopes of lines. Avery said, The easiest way to find the slope is to divide y by x. The slope of this line is or MGSE8.EE.6 Show another way to find the slope of the line that passes through the points listed in the table. Your way must be different from Avery s way MGSE8.EE.7a 1. Determine whether the following equation has one solution, no solution, or infinitely many solutions: Infinitely many solutions Only one solution Two solutions No solution MGSE8.EE.7a 2. Solve the following equation: X Y X Y Infinitely many solutions X Y X Y No Solution.

6 MGSE8.EE.7b 3. Find the solution to the following equation: MGSE8.EE.7b 4. Solve the following equation for the given variable: MGSE8.EE.7.b 1. Solve the equation to the right for the given variable

7 MGSE8.EE.7.b 2. Solve the equation to the right for the given variable MGSE8.EE.7b 14. Solve the given equation for the variable k (6 5k) + 32 = 24k MGSE8.EE.7b 15. Solve the equation on the right for x (5x 2) = 6(6x 1) MGSE8.EE.8.a 3. What is the intersection between the two equations that are graphed on the coordinate plane?

8 MGSE8.EE.8.a 4. Write the equations that are represented by the two lines that intersect at the point. MGSE8.EE.8.a 5. Which graph on the right shows the intersection between the 2 lines below? MGSE8.EE.8.a 6. Which graph on the right shows the intersection between the 2 lines below?

9 MGSE8.EE.8.a 7. Which graph on the right shows the intersection between the 2 lines below? MGSE8.EE.8.a 8. Which point is the solution to both equations shown on the graph to the right? MGSE8.EE.8.b 9. If and, then what is the value of x?

10 MGSE8.EE.8.b 10. If and what is the value of y? MGSE8.EE.8.b 11. If and, then what is equal to?

11 MGSE8.EE.8.b 12. If and, then what is equal to? MGSE8.EE.8.b 13. Solve the system of equations on the right algebraically. MGSE8.EE.8.b 14. Solve the system of equations algebraically.

12 MGSE8.EE.8.b 15. Solve the system of equations algebraically. MGSE8.EE.8.c 16. The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. Which pair of equations can be used to determine c, the number of children, and a, the number of adults who attended the fair? MGSE8.EE.8.c 17. Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Which system of equations could be used to determine the cost of 1piece of fudge, f, and 1 piece of bubble gum, g?

13 MGSE8.EE.8.c 18. At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Determine t, the cost of a taco, and m, the cost of a small glass of milk? MGSE8.EE.8.c 19. Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket, s and one child, c ticket? MGSE8.EE.8.c 20. A group of adults and kids took a trip to the circus. One adult ticket cost $15 and one child ticket cost $10. If the total admission cost for the group of 25 was $300, then how many children, c, and how many adults, a, attended the circus trip? MGSE8.F Which table of values represents a function and why? Table A, because each input goes to multiple outputs. Table A Table B

14 Table A, because each output goes to only one input. Table B, because each input goes to exactly one output. Table B, because each output value is greater than the input values. MGSE8.F Write the ordered pairs suggested by the mapping. Is the given relation a function? {(5, 4), (5, 1), (-3, -4), (-3, -2)}; the relation is not a function. {(5, 1), (4, 5), (-3, -4), (-2, -3)}; the relation is a function. {(4, 5), (1, 5), (-4, -3), (-2-3)}; the relation is a function. {(5, 4), (5, 1), (-3, -4), (-3, -2)}; the relation is a function. MGSE8.F What is the domain of the function to the right? {2, 3, 5, 6} {0, 1, 2, 3) {(0, 2), (1, 2), (2, 5), (3, 6)} {(2, 0), (2, 1), (5, 2), (6, 3)} MGSE8.F Look at the two relations to the right. Which of the following correctly compares the two relations? Neither relation A nor relation B is a function. Relation A has repeated y-values, and relation B has repeated x-values. Both relation A and relation B are functions as each x-value corresponds to a unique y- value. Relation A is a function as each x-value corresponds to a unique y-value. Relation B is not a function as each x-value does not correspond to a unique y-value. Relation A is not a function as each x-value does not correspond to a unique y-value. Relation B is a function as each x-value {(0, 2), (1, 3), (2, 5), (3, 6)}

15 corresponds to a unique y-value. MGSE8.F Given the equation: y 3x 5, and the following input values : ( -2, -1, 0, 1, 2), which table assigns the proper output values to the given inputs. Table A Table B Table C Table D MGSE8.F In which table is y a function of x. Table A Table B Table C Table D MGSE8.F Which of the following could be the graph of a function? Graph A Graph B Graph C Graph D MGSE8.F If the pattern in the table continues, what % of charge will the video game battery have after 60 X Y X Y X Y X Y

16 minutes of charging? MGSE8.F Write the inverse of the relation to the right. {(6, -1), (3, - 2), (0, -3), (-3, -4), (-5, -5)} {(1, -6), (2, -3), (3, 0), (4, 3), (5, 6)} {(-1, -6), (-2, -3), (-3, 0), (-4, -3), (-5,-6)} {(-1,6), (-2, 3), (-3,0), (-4, -3), (-5, -6)} MGSE8.F Rain is flowing into two containers at different rates. The figures to the right show the volume of water in each container at different times. What is the difference in the rate of change between the two containers? 1 gallons per minute 5 3 gallons per minute 5 5 gallons per minute 2 15 gallons per minute 2 MGSE8.F Compare the following functions to determine which has the greater rate of change. {(-6, 1), (-3, 2), (0, 3), (3, 4), (6, 5)} Function 1: y = 2x + 4 Function 2: The rate of change for function 1is 3; the rate of change for function 2 is 2; Function 1 has the greater rate of change. The rate of change for function 1 is 2; the rate of change for function 2 is 3; Function 2 has the greater rate of change. The rate of change for function 1 is -2; the rate of change for function 2 is -3; Function 1 has the greater rate of change. The rate of change for function 1 is -3; the rate of change for function 2 is -2; Function 2 has the greater rate of change. MGSE8.F.2 Function 1: Gift Card: Samantha starts with $20 on a gift

17 27. Compare the two linear functions and determine the slopes of both. Function 1, the amount decreases by $4.50 each week, while in function 2, the amount increases $10.00 each month. Function 1, the amount increases $3.50 each week, while in function 2, the amount decreases $5.00 each month. Function 1, the amount decreases $3.50 each week, while in function 2, the amount increases $5.00 each month. Function 1, the amount decreases $5.00 each week, while in function 2, the amount increases $3.50 each month. MGSE8.F Which table displays the same rate of change as the equation: y 4x 5, and correctly models the equation. Table A Table B Table C Table D card for the bookstore. She spends $3.50 per week to buy a magazine. Let y be the amount remaining as a function of the number of weeks, x. Function 2: Calculator rental: The school bookstore rents graphing calculators for $5 per month. It also collects a non-refundable fee of $10.00 for the school year. Write the rule for the total cost (c) of renting a calculator as a function of the number of months (m). c = m X Y X Y X Y X Y

18 MGSE8.F The total cost in dollars, y, of a membership at each of four health clubs is represented in terms of x, the number of months of the membership. Which representation has the greatest rate of change? Health Club A Health Club B Health Club C Health Club D MGSE8.F Which of the following describes the correct rate of increase for each person? Sarah's distance increased 2 miles per week, and James's distance increased 3 miles per week. James had a higher rate of increase than Sarah. Sarah's distance increased 1mile per week, and James's distance increased 2 miles per week. James had a higher rate of increase than Sarah. Sarah's distance decreased 2 miles per week, and James's distance decreased 3 mile per week. Sarah had a higher rate of increase than James. Sarah's distance increased 3 miles per week, and James's distance increased 2 miles per week. Sarah had a higher rate of increase than James.

19 MGSE8.F Look at the two functions. Which of the following correctly compares the two functions? Both functions are linear. Function 1 has a greater rate of change than function 2. Both functions are linear. Function 2 has a greater rate of change than function 1. Both functions are linear and have the same rate of change. Neither function is linear as neither involves a constant rate of change. MGSE8.F Which of the following correctly explains which ball was traveling faster, and how much faster the faster ball was traveling? The slope of each function represents the ft. per sec.. Since the slope of the graph is 1 88 ft/sec and the slope of the equation is 1 88 ft/sec, pitcher A s ball is traveling faster by a rate of 1 ft/sec. 880 The slope of each function represents the seconds per feet. Since the slope of the graph is 1 sec/ft and the slope of the equation 80 is 1 sec/ft, pitcher A s ball is traveling 88 faster by a rate of 1 sec/ft. 880 Pitcher A Pitcher B The distance traveled in feet by a ball pitched by pitcher B can be shown using the equation: d = 88t. The variable t represents time in seconds after the ball was pitched. The slope of each function represents the seconds per feet. Since the slope of the graph is 80 sec/ft and the slope of the equation is 88 sec/ft, pitcher B s ball is traveling faster by a rate of 8 sec/ft. The slope of each function represents the feet per second. Since the slope of the graph is 80 ft/sec and the slope of the equation is 88 ft/sec, pitcher B s ball is traveling faster by a rate of 8 ft/sec.

20 MGSE8.F Look at the functions to the right. Which of the following correctly compares the two functions? Both functions are linear. Function 1 has a greater rate of change than function 2. Both functions are linear. Function 2 has a greater rate of change than function 1. Both functions are linear and have the same rate of change. Neither function is linear as neither involves a constant rate of change. 34. Which of the following functions is non-linear? y 2x 1 2x 2y 14 ( x 2) 2 6 x 7 MGSE8.F.3 y 3x Which of the following functions is non-linear? MGSE8.F.3 X Y X Y X Y X Y Which of the following functions is linear? MGSE8.F.3

21 37. Does the table represent a linear or non-linear function? Explain. MGSE8.F.3 Linear. The rate of change is constant. Non-Linear. The rate of change is not constant. Linear. The rate of change is not constant. Non-Linear. The rate of change is constant. 38. Does the graph represent a linear or non-linear function? Explain. MGSE8.F.3 Linear. The rate of change is constant between all of the points on the graph. Linear. The rate of change is not constant between all of the points on the graph. Non-linear. The rate of change is constant between all of the points on the graph. Non-linear. The rate of change is not constant between all of the points on the graph. 39. The table at the right represents a linear function. What is the slope? MGSE8.F

22 40. Find the slope, m, and y-intercept, b, of the graph to the right. MGSE8.F.3 m = 2, b = - 3 m = - 2, b = 1 m = 3, b = - 2 m = - 3, b = - 2 MGSE8.F4 1. Mr. Ellison needs to drain his above ground pool before the winter. The graph below represents the relationship between the number of gallons of water remaining in the pool and the number of hours that the pool has drained? Determine the rate of change for this relationship. Explain what the rate of change means in this particular situation. Determine the initial value for this relationship. Explain what initial value means in this particular situation. MGSE8.F4 2. The junior class has paid $100 to a disc jockey for a dance. Tickets for the dance are $4 each. Express the net income as a function of the number of tickets sold.

23 MGSE8.F4 3. Brenda is on a pay as you go cell phone plan. The graph on the right shows how much she pays per hour of usage. How much does Brenda s pay per hour to use her cell phone? MGSE8.F4 4. Alicia and Melissa did jumping jacks. The table shows the number of jumping jacks that Alicia did in different amounts of time. The graph shows the number of jumping jacks Melissa did in different amounts of time. Which choice best describes the difference between the rates at which the girls did jumping jacks? Melissa s Jumping Jacks Record Melissa did 6 more jumping jacks per minute than Alicia. Alicia did 6 more jumping jacks per minute than Melissa. Melissa did 5 more jumping jacks per minute than Alicia. Alicia did 5 more jumping jacks per minute than Melissa. MGSE8.F5 5. Mr. Jones filled his swimming pool with water. Mr. Jones began filling the pool at a constant rate. He turned off the water for a while. He then turned the water back on at a slower constant rate. Mr. Jones turned off the water again for a while. He then turned the water back on at the first rate. Which graph best represents Mr. Jones filling the pool?

24 MGSE8.F5 6. Tom went to the grocery store. The graph below shows Tom s distance from home during his trip. Tom stopped twice to rest on his trip to the store. What is the total amount of time that he spent resting? 5 minutes 7 minutes 8 minutes 10 minutes MGSE8.F5 7. Each day, Maria walks from home to school and then from school to home. The graphs that follow show the distance that Maria is from home at different times during the walk. Match the graphs to the descriptions of Maria s walk shown to the right of the graphs. Next to each graph, enter the letter (a, b, c, or d) of the description that best matches the graph. a. b. c. d. MGSE8.F5 8. A bicycle club went on a six-hour ride. The graph below shows the relationship between the number of hours spent on the trails and the number of miles traveled. Which statement best interprets information provided by the graph?

25 The club members rode at a constant speed for the entire ride. The club members stopped for a rest during their ride. The number of miles traveled increased continuously throughout the ride. The number of miles traveled increased some of the time and decreased some of the time.