Class: Date: Math 10 - Unit 6 - Functions - UNIT REVIEW WORKSHEET Multiple Choice Identify the choice that best answers the question. 1. Which set of ordered pairs does not represent a function? Ï i) Ì Á 4,7 ˆ, Á5,10ˆ, Á6,13ˆ, Á 4,1 ˆ Ó Ï ii) Ì Á 6,8 ˆ, Á7, 9ˆ, Á9,11ˆ, Á 10, 12 ˆ Ó Ï iii) Ì Á 1, 10 ˆ, Á1, 8ˆ, Á0,7ˆ, Á 2,9 ˆ Ó Ï iv) Ì Á 9,0 ˆ, Á6,1ˆ, Á 8,7ˆ, Á 10,0 ˆ Ó a. i b. ii c. iv d. iii 2. Identify the domain of this relation. Ï Ì Á 10,12 ˆ, Á7,9ˆ, Á11, 13ˆ, Á 8, 10 ˆ Ó a. { 10,9,11,12} b. { 13, 10,9,12} c. { 7,8,10,11} d. { 7,8,11,12} 3. This table shows the profit, P dollars, of different numbers of people attending a carnival, n. Identify the range. Number of People, n Profit, P ($) 1 12.50 2 25.00 3 37.50 4 50.00 5 62.50 a. { 1, 2, 3, 4, 5,...} b. { 12.50, 25.00, 37.50, 50.00, 62.50,...} c. { 1, 2, 3, 4, 5, 12.50, 25.00, 37.50, 50.00, 62.50} d. { 1, 12.50, 2, 25.00, 3, 37.50, 4, 50.00, 5, 62.50,...} 4. For the function f( x) = 4x + 2, determine f( 5). a. 10 b. 7 c. 22 d. 0 5. For the function f( x) = x 8, determine x when f( x) = 16. a. 56 b. 40 c. 8 d. 8 1
6. Identify the independent variable and the dependent variable for this table of values. Time, t Money Earned, M ($) 4 38.00 5 47.50 9 85.50 20 190.00 30 285.00 a. independent variable: M dependent variable: t b. independent variable: domain dependent variable: range c. independent variable: money earned dependent variable: time d. independent variable: time dependent variable: money earned 7. This is a graph of the function g( x) = 3x + 2. Determine the domain value when the range value is 2. a. 0 b. 2.5 c. 1 d. 0 2
8. Which of these graphs represents a function? i) ii) iii) iv) a. ii b. i c. iii d. iv 3
9. Which of these graphs represents a function? i) ii) iii) iv) a. iv b. ii c. i d. iii 10. Determine the range of the graph. a. 5 y 3 b. 3 y 3 c. 5 x 1 d. 3 y 1 11. Which of the following expressions is interval notation for a domain of 4 x < 12 a. ( 4, 12 ) b. [ 4, 12 ] c. ( 4, 12 ] d. [ 4, 12 ) 4
12. Which of the following expressions is interval notation for a domain of 6 < x 2 a. ( -6, -2 ) b. [ -6, -2 ] c. ( -6, -2 ] d. [ -6, -2 ) 13. A person in a car drives away from a stop sign, cruises at a constant speed, and then slows down as she approaches another stop sign. Which graph best represents this situation? a. c. b. d. 5
14. This graph shows the height of the tide in a harbour as a function of time in one day. What is the greatest height of the tide? a. 9 m b. 2 m c. 8 m d. 4 m 6
15. This graph shows the height of the tide in a harbour as a function of time in one day. Which statement best describes the tide at Point C? a. The tide is at its greatest height. b. The tide is at its least height. c. The tide is 7.1 m high. d. The tide is 4 m high. 16. This graph shows the free-fall speed of a skydiver as a function of time. Which statement best describes what is happening for line segment BC in the graph? a. The skydiver landed on the ground. b. The skydiver opened her parachute. c. The skydiver was free-falling. d. The skydiver jumped out of the plane. 7
17. Gail leaves the house for her morning jog. She stops for a quick drink, then continues jogging before stopping again to chat with a friend. She then jogs back home. Which graph best represents Gail s run? 8
a. b. c. d. 9
18. The altitude of a plane, a metres, is related to the time, t minutes, that has elapsed since it started its ascent. Determine the rate of change of this linear relation. t (min) 0 2 4 6 8 a (m) 4000 5400 6800 8200 9600 a. 1500 m/min b. 1400 m/min c. 1200 m/min d. 700 m/min 19. Minerva has $100. This graph represents the money Minerva would have if she purchased different numbers of CDs. Determine the rate of change of the relation. a. $10 /CD b. $20 /CD c. $10 /CD d. $14.29 /CD 20. The relation between x and y is linear. Which ordered pair completes this table of values? x y 7 4 4 7 1 10 2 13 a. ( 5, 16) b. ( 16, 5) c. ( 13, 5) d. ( 5, 13) Short Answer You must clearly show your process and box your final answer. 21. For the function g( x) = 4 x + 2, determine x when g x 3 ( ) = 14. 22. a) Write in function notation: h = x 4 b) Write as an equation in two variables: k(x) = 2x 7 10
23. For the function p( x) = 3x 2 1, determine x when p( x) = 11. 24. For the functions f( x) = 6x 3 and g(x) = 2x + 1 determine x when f(x) = g(x). 25. For the function t(x) = 2x 2 6x + 1, find t( 5a) 26. Determine the domain and range of the graph of this function. 27. State the domain and range of the following function using interval notation. 28. Which equations represent linear relations? Create tables of values if necessary. a) 5x y = 8 d) y = x 2 + 29x 30 b) x 2 + y 2 = 11 e) y = x 3 + 8 c) x = 7 6y f) y 5 = 0 29. This table represents the approximate relation between a distance in miles and the same distance in kilometres. Determine the rate of change of the relation.. Miles (mi.) 9 18 27 36 45 Kilometres (km) 14.4 28.8 43.2 57.6 72.0 11
30. Which graphs have: i) a negative rate of change? ii) a positive rate of change? iii) neither a negative nor a positive rate of change? a) b) c) d) e) f) 12
Problem 31. Graph the data provided in the table of values. a) Will you join the points? Why or why not?. b) Does the graph represent a function? Explain. Number of Tickets, t Cost, C ($) 30 10 45 15 75 20 90 25 120 30 13
Math 10 - Unit 6 - Functions - UNIT REVIEW WORKSHEET Answer Section MULTIPLE CHOICE 1. A 2. C 3. B 4. C 5. C 6. D 7. D 8. D 9. C 10. B 11. D 12. C 13. D 14. C 15. D 16. B 17. C 18. D 19. C 20. A SHORT ANSWER 21. -9 22. a) h(x) = x 4 b) k = 2x 7 23. x = 2, -2 24. x = 1/2 25. 50a 2 + 30a + 1 26. Domain: 4 x < 3 Range: 3 y < 4 27. Domain: [ 4,3) Range: ( 3,4] 28. The relations in parts a, c, and f are linear. 29. approximately 1.6 km/mi. 30. i) Graphs b and d have a negative rate of change. ii) Graphs a and e have a positive rate of change. iii) Graphs c and f have neither a negative nor a positive rate of change. 1
PROBLEM 31. a) The points are not joined because the data are only valid for whole numbers of tickets. b) The relation is a function because there is only one cost for each number of tickets. 2