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Lesson 6.1: Graphs of Relations Workbook 6A Lesson 6.1: Graphs of Relations Explore Your Understanding Assignment 1. The graph shows the number of students taking each of five different types of transportation to get to school. Type of School Transportation for Students Go Number 50 of Students an - - - - 20 10 Foot Bike Bus Train Car Type of Transportation 1 a. Use the data in the graph to represent the relation as a set of ordered pairs. 1 b. What do the horizontal and vertical axes represent? 2 c. State two conclusions about the relation represented in the graph.Workbook 6A Lesson 6.1: Graphs of Relations 2. A relation is defined by the ordered pairs ((5, 25), (6, 30), (7,35), (8, 40)}. 2 a. State two relationships about the relation. 1 b. Assuming the relation continues with the same relationship, state the two sets of ordered pairs that follow (8,40). 3. The table and graph provided show the speed of a hot air balloon at one second intervals from the time of lift-off. Hot Air Balloon Speed Time, r Speed, S 20.0 (s) m/s 0 0 . G 15.0 1 1.8 12 5 4.5 Spoon [mis) 10.0 AWN 9.7 7.5 11.4 14.8 16.3 2.5 10 16.3 5 6 B 9 10 11 Time (5) 1 a. What does point 4 represent on the graph?Lesson 6.1: Graphs of Relations Workbook 6A 2) b. Interpolate the speed of the balloon half-way between points E and F. Explain. (2) C. Extrapolate the speed of the balloon at 11 seconds of flight. 4. A graph representing Jason's distance from home, on a bike ride, is shown. Jason's Bike Ride Distance from Home (kmi 10 20 30 50 60 70 80 90 100 110 120 Time (min) 1 a. During his trip, Jason stopped to play at the park with a friend. Which segment of the graph best represents this part of his trip? Explain.Workbook 6A Lesson 6.1: Graphs of Relations 1 b. How much time did Jason spend at the park? 1 C. Which statement best describes segment DE? Explain. i. Jason spends time at the park. ii. Jason leaves home. iii. Jason cycles to the park. iv. Jason returns home. 5. It takes 15 minutes for the interior temperature of an oven to rise from 20"C to 180"C. A cake is placed in the oven for 25 minutes. When the cake is removed, the oven is turned off. The interior temperature of the oven returns to 20'C after 15 minutes. The oven is then turned on again, 45 minutes later. It takes 10 minutes for the temperature to reach 165"C. Cookies are placed in the oven to bake for 20 minutes. When the cookies are removed, the oven is turned off. The interior temperature of the oven returns to 20'C after 10 minutes. 4 a. Sketch a graph of the scenario.Lesson 6.1: Graphs of Relations Workbook 6A (3 b. Label each section of the graph and explain what each one represents.Lesson 6.2: Domain and Range Workbook 6A Lesson 6.2: Domain and Range Explore Your Understanding Assignment (8 ) 1. Determine the domain and range of the following relations using set builder notation. a. b. -2 D: D: R: R:Workbook 6A Lesson 6.2: Domain and Range 2. Match the interval notation below to the relations represented in Question I. 1 a. Domain: [-3,4] and Range: (-ce, 3] Relation: 1 b. Domain: (-co, 4] and Range: (-09,3] Relation: 3. Identify the independent and dependent variables in the following scenarios. Explain each choice. 3 a. The number of bacteria in relation to time. Independent variable - Dependent variable- (3) b. The total cost of tickets for a concert in relation to the number of tickets purchased. Independent variable - Dependent variable -Lesson 6.2: Domain and Range Workbook 6A 4. The graph shows the volume, I', of gasoline left in a car's tank after a distance travelled, d, in hundreds of kilometres. Rate of Fuel Consumption 72 Fuel in Tank IL 12 100 200 300 400 500 700 +d Distance (km) 2 a. Determine the domain and range of the relation using set builder notation or interval notation. (2 b. Is the data represented by the relation continuous or discrete? Explain.Workbook 6B Lesson 6.3: Linear Relations Lesson 6.3: Linear Relations Explore Your Understanding Assignment (2) 1 . The relation represented in the table is linear. Which number would complete this table? Explain. X 3 7 11 15 19 20 14 8 (2) 2. Larry and Laura are discussing the following table of values. 4 6 8 10 2 7 12 17 I think the table Thinkstock Who is correct? Explain. does not represent a linear relation. I believe it does3. A grade 10 science class does a controlled experiment involving a heat lamp and a block of 4. The table of values provided represents a linear relation. ice on a black coloured plastic mat. This mat has a drain hole for the water and also sits on a kilogram weigh scale. This graph represents the time it takes to melt the 4.0 kg block of ice to Time (s) 0 2 3 4 nothing. Distance (m) 0 5 10 15 20 Melting of a Block of Ice 2 a. Determine the slope of the graph of the relation. 4.5 40 3.6 -- 3.0 (kal 25 20 1.5 1.0 3 b. Graph the relation. 10 20 30 40 50 60 70 80 90 Time (minutes) a. Determine the mass of the block of ice after 35 minutes. 2 b. Determine the rate of change of the mass of the ice-block per minute.Lesson 6.3: Linear Relations Workbook 6B Workbook 6B Lesson 6.3: Linear Relations (3) 5. A snail begins its trek 3 m from home and continues travelling away from home at a rate of 1) 6. Which of the following graphs has a rate of change of 3 m/h and a starting point of 1 m? 4 m/h. Sketch a graph representing this scenario. A. C. Distance Distance (m) 5 5 Time (h) Time (h) B. D. Distance Distance (m) (m) 5 5 6 Time thy Time (h)Lesson 6.3: Linear Relations Workbook 6B Workbook 6B Lesson 6.3: Linear Relations 7. The graph below tracks the descent of a skydiver with an open parachute at 1200 m high. Ken 1 b. Explain why the second attempt does not work out to be the correct rate of change either. made two attempts to determine the rate of change of the descent of the parachutist because his first attempt did not make sense to him. Descent of a Skydiver 1 300 1 200 1 100 1 000 Height 900 Above 800 (2) c. Determine the correct rate of change. Ground 700 600 500 300 200 100 2 8 9 10 11 12 13 14 15 16 Time (min) Ken's first attempt at the rate of change: Ken's second attempt at the rate of change: m = rise run run P = m = 2 y 1 - X STEP 1: STEP 1: 2 d. Explain what the rate of change means in terms of the skydiver's decent. m = 1 15 - 1200 m = 1 1200 - 0 0-0 15-0 STEP 2: STEP 2: m = -1185 m = _ 1 200 0 15 m = undefined m = 80 m/ min 1 a. Explain why the first attempt did not make sense to Ken.Lesson 6.4: Linear Functions Workbook 6B Workbook 6B Lesson 6.4: Linear Functions 2. If A(x) = 4x - 11, determine A list of numbers is given. 2 a . f ( ) -9,1,0, - 7,5, 1 Using any combination of the numbers, (1 a. generate a set of ordered pairs that represents a function. 1 b. generate a set of ordered pairs that does not represent a function. 2 b. f(-3 ) 4. The equation C = 10n + 45 represents the total cost, C dollars, for a sports banquet, when n people attend. 2 a. Describe the function in words and then express the function using function notation. 2 c. x if f(x) = 53 3 b. Determine C(250) and explain what the result represents.Lesson 6.4: Linear Functions Workbook 6B 2 If the total cost of the banquet is C(n) = 4 295, find n, the number of people attending the banquet.Workbook 6B Lesson 6.4: Linear Functions Lesson 6.4: Linear Functions Explore Your Understanding Assignment (4) 1. Determine whether the relations below represent functions. Explain how you know. Relation How you know: {(-2,3),(-5,10),(-7, 16),(-9,22)} 1 2 3 4 cat dog # short hair guinea pig - long hair 20 ADLC Mathematics 10C