Relations & Functions Practice Test

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1 Relations & Functions Practice Test 1. Consider the relation represented b this graph. Represent the relation as a set of ordered pairs. Distance (km) Distances Jogged in a Da Josh Koko Ton Shadi Jodi Student a. {(Josh, 8), (Koko, 5), (Ton, ), (Shadi, 11), (Jodi, 7)} b. {(8, Josh), (5, Koko), (Ton, ), (11, Shadi), (Jodi, 7)} c. {(8, Josh), (5, Koko), (, Ton), (11, Shadi), (7, Jodi)} d. {(Josh, 8), (Koko, 5), (Ton, ), (Shadi, 7), (Jodi, 11)}. Capital cities can be associated with the province or territor the are in. Capital Cit Province/Territor Victoria British Columbia Edmonton Alberta Regina Saskatchewan Winnipeg Manitoba Whitehorse Yukon Yellowknife Northwest Territories Iqaluit Nunavut Describe this relation in words. a. The relation shows the association is the capital of from a set of capital cities to a set of provinces and territories. b. The relation shows the association is the largest cit of from a set of capital cities to a set of provinces and territories. c. The relation shows the association is the capital of from a set of provinces and territories to a set of capital cities. d. The relation shows the association is in the province/territor of from a set of provinces and territories to a set of capital cities.

2 3. A person in a car drives awa 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. Speed (km/h) Speed (km/h) Time (min) Time (min) b. d. Speed (km/h) Speed (km/h) Time (min) Time (min). This graph shows the free-fall speed of a skdiver as a function of time. At what speed was the skdiver travelling 1 s before she reached the ground? 16 Free-Fall Speed of a Skdiver A B 1 Speed (km/h) 8 O D C E Time (s) a. km/h b. 1 km/h c. 3 km/h d. 1 km/h

3 5. Which of these graphs represents a function? i) ii) x x iii) iv) x x a. ii b. i c. iii d. iv 6. This graph shows the cost of hosting a dance, c, as a function of the number of students attending, n. What is a restriction on the domain? c Cost of Hosting a Dance 3 Cost ($) n Number of Students a. The domain can onl contain positive numbers. b. The domain can onl contain whole numbers between 1 and 35. c. The domain can onl contain whole numbers. d. The domain can onl contain whole numbers that are multiples of 5.

4 7. Each graph below shows distance, d metres, as a function of time, t hours. Which graph has a rate of change of m/h and a vertical intercept of 3 m? a. 1 d c. 1 d 8 8 Distance (m) 6 d = k(t) Distance (m) 6 d = g(t) 6 8 t Time (h) 6 8 t Time (h) b. 1 d d. 1 d 8 8 Distance (m) 6 d = f(t) Distance (m) 6 d = h(t) 6 8 t Time (h) 6 8 t Time (h) 9. For the function, determine.

5 1. For the function, determine x when. 11. How can ou tell that this graph represents a function? Cost of Hosting a Dance 3 Cost ($) Number of people 1. Explain wh the points on this graph are not joined. Cost of Hosting a Dance 3 Cost ($) Number of people

6 c) 13. This is a graph of the function. h(x) = 1/x + 1 x a) Determine the range value when the domain value is. b) Determine the domain value when the range value is Determine the domain and range of the graph of this function. = f(x) x 6

7 15. A student drew a graph to represent this situation. Lenora starts her 3.5-km walk home from school. After walking 1 km in min, she stops to talk to a friend. She talks for 1 min and then continues walking at the same pace. Fifteen minutes later, she stops for 5 min to rest. She starts walking at the same pace again and after 15 min, she decides to jog the rest of the wa home. Describe an errors in the student s graph. Sketch the correct graph. 3.5 Lenora's Walk Home 3 Distance from home (km) Time (min)

8 16. A helicopter is travelling toward its destination. Time (min) Distance from Destination (mi.) a) Identif the dependent and independent variables. b) Use the table of values to determine whether the relation is linear. Justif our answer. c) If the relation is linear, determine its rate of change. d) Write an equation for this relation.

9 17. This graph shows the distance, d kilometres, from Beijing, China, to Edmonton, Alberta, as a function of fling time, t hours. 9 d Flight from Beijing Edmonton Distance (km) t Time (h) a) Determine the vertical and horizontal intercepts. Write the coordinates of the points where the graph intersects the axes. Describe what the points of intersection represent. b) Determine the rate of change. What does it represent? c) Write the domain and range: d) What is the distance to Edmonton when the plane has been fling for 5 h? e) How man hours has the plane been fling when the distance to Edmonton is 65 km?

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