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NAME:___________________________________ Date _____________________ Period _________ Math 8 Unit 4 Functions Summative Assessment (Advanced) 1. Which relation below is a function? (MCC.8.F.1) a. {(1, 2), (3, 5), (3, 8), (4, 9)} b. {(-1, 3), (0, 7), (3, 7), (6, 6)} c. {(2, 1), (2, 2), (2, 3), (2, 4)} d. {(-8, 3), (3, -8), (5, 10), (5, 8)} 2. Tell whether the relation is a function. Explain why or why not. If the relation is not a function, provide a counterexample. (MCC.8.F.1) 3. Tell whether the relation is a function. Explain why or why not. If the relation is not a function, provide a counterexample. (MCC.8.F.1) 4. Tell whether the relation is a function. Explain why or why not. If the relation is not a function, provide a counterexample. (MCC.8.F.1) 1 2 2 3 3 4 5. Tell whether the relation is a function. Explain why or why not. If the relation is not a function, provide a counterexample. (MCC.8.F.1) π = ππ + π 6. Tell whether the relation is a function. Explain your yes or no answer. If the relation is not a function, provide a counterexample. (MCC.8.F.1) ππ = π In problems 7-9 determine which function has a greater rate of change. Justify your answer. (MCC.8.F.2) 7. Function 1: y = 3x + 5 Function 2 : y = 5x + 3 8. Function 1: (2, 2) (3, 3) (4, 4) (5, 5) Function 2: y = x + 1 9. Function 1: Function 2: x y -1 6 0 3 1 0 2 -3 10. Which of the following is a function? Justify your answer. (MCC.8.F.1) A. B. C. D. x 1 1 2 x 2 1 2 x 1 2 3 x 1 1 1 y 2 3 4 y 2 3 4 y 3 3 3 y 2 3 4 11. Which mapping diagram is not a function? Justify your answer. (MCC.8.F.1) A. B. C. D. 1 2 1 1 2 2 1 1 1 1 2 2 2 12. Which Graph is a function? Justify your answer. (MCC.8.F.1) a. B. C. D. 13. Which equation is not a function? Justify your answer. (MCC.8.F.1) A. B. C. D. π¦ = |π₯ + 4| β 3 π¦ = π₯2 + 4 π¦ = β3 1 π₯=5 14. For each of the following situations, create a table and a graph to model the relationship. Then describe the situation as increasing or decreasing, and linear or nonlinear. a. Mike has $25. He saves $11 each week. x y b. Nettie has $2. She triples her money each week. x y c. Paul has $100. He spends $5 each day. x y For each of the following problems, complete the other representations for the situation. 16. Table x (days) 0 Make the Graph y(meals) 0 1 3 2 6 3 9 4 12 What is the rate of change (slope)? What is the start point?(constant) What is the equation? What is the story? 17. x( Fill in the table ) y( Graph ) What is the rate of change (slope)? What is the start point?(constant) What is the equation? What is the story? Answer Key: 1. b 2. Yes, because each x(input) has one unique y(output). 3. No, because when you apply a vertical line there are two points that touch (vertical line test); there are two xβs for more than one y (the xβs repeat). Counterexample: If the graph were turned pointing up or down instead of to the left (rotated 90 degrees it would be a function) 4. No, because the 3 repeats in the domain [for (3,3) and (3,4)]. Counterexample: If you changed it to (4,4) and (3,3) it would be a function. 5. Yes, because the constant is that itβs being multiplied by three every time 6. Yes, because each x only has one y. (It would be a curved line increasing from the origin.) 7. Function 2 because the rate of change (slope) is 5, which is greater than 3. 8. Neither, they are equal because the rate of change (slope) is 1 for each. 9. Function 1 is greater because the rate of change (slope) is -3, which is greater than 1. 10. c, because none of the x values repeat. 11. d, because the x values have more than one y value and you would get (1,1) and (1,2) 12. a, because it is a horizontal line none of the x values repeat 13. d, because all of the x values would be 5 (they would repeat, making a vertical line) 14. a) Table: (0,25) (1,36) (2,47) (3,58) (4,69); Graph: Slope of 11, y-intercept at (0,25). It is linear and it is increasing b) Table: (0,2) (1,6) (2,18) (3,54) (4,162); Graph: y-intercept at (0,2),. It is nonlinear ( increasing ) and it is c) Table: (0,100) (1,95) (2, 90) (3,85) (4,80); Graph: Slope -5, y-intercept at (0,100). It is linear and it is decreasing 16. Table: already done; Slope is 3, Starts at 0, Equation y=3x; Graph: Line with slope of 3 starting at the origin; Story: You eat 3 meals every day 17. Table: x(seconds) and y(words)-possible answers for x: 0,1,2,3,4,5 and y:5,10,15,20,25,30 ; Slope is 5, Starts at 0, Equation y=5x; Graph: already done; Story: You can read 5 words each/per second