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Math 10 Unit 5 Relations and Functions Name:_____Key_________ Assignment: 5.2 1. Which arrow diagrams represent functions? 2. Which sets of ordered pairs represent functions? Identify the domain and range of each set of ordered pairs. a) {(1, 3), (2, 6), (3, 9), (4, 12)} Function; domain: {1, 2, 3, 4}; range: {3, 6, 9, 12} b) {(1, 0), (0, 1), (–1, 0), (0, –1)} Not a function; domain: {–1, 0, 1}; range: {–1, 0, 1} c) {(2, 3), (4, 5), (6, 7), (8, 9)} Function; domain: {2, 4, 6, 8}; range: {3, 5, 7, 9} d) {(0, 1), (0, 2), (1, 2), (0, 3), (1, 3), (2, 3)} Not a function; domain: {0, 1, 2}; range: {1, 2, 3} 3. Write in function notation. a) C = 20n + 8 C(n) = 20 n + 8 c) t = 5 d t(d) = 5 d b) P = n – 3 P(n) = n – 3 d) y = – x f(x) = – x 4. Write as an equation in two variables. a) d(t) = 3t – 5 b) f (x) = –6x + 4 d = 3t – 5 y = –6x + 4 c) C(n) = 5 n d) P(n) = 2n – 7 C=5n P = 2n – 7 5. For each relation below: ■ Determine whether the relation is a function. Justify your answer. ■ Identify the domain and range of each relation. a) {(1, 1), (2, 8), (3, 27), (4, 64)} Function, it is one to one. domain: {1, 2, 3, 4}; range: {1, 8, 27, 64} b) {(3, 4), (3, 5), (3, 6), (3, 7)} Not a function because 1 domain matches to 3 different ranges. domain: {3}; range: {4, 5, 6, 7} 6. For each table of values below: i) Explain why the relation is a function. ii) Identify the independent variable and the dependent variable. Justify your choices. iii) Write the domain and range. Function because each domain matches a different range. (1 to 1) Independent variable: Number of cans of juice purchased. Dependent variable: Cost. Domain: {1, 2, 3, 4, 5, 6 }; range: {2.39, 4.00, 6.39, 8.00, 10.39, 12.00 } Function because each domain matches a different range. (1 to 1) Independent variable: Altitude. Dependent variable: Temperature. Domain: {610, 1220, 1830, 2440, 3050, 3660 }; range: {15.0, 11.1, 7.1, 3.1, –0.8, –4.8 } 7. For the function f (x) = – 5x + 11, determine: a) f (1) b) f (–3) f (1) = – 5(1) + 11 = 6 f (–3) = – 5(–3) + 11 = 26 c) f (0) d) f (1.2) f (0) = – 5(0) + 11 = 11 f (1.2) = – 5(1.2) + 11 = 5 8. a) For the function f (n) = 2n – 7, determine n when: i) f (n) = 11 ii) f (n) = – 6 11 = 2n – 7 – 6 = 2n – 7 b) For the function g(x) = – 5x + 1, determine x when: i) g(x) = 41 ii) g(x) = – 16 41 = – 5x + 1 –16 = – 5x + 1 9. The function C(i) = 2.54 i converts a measurement of i inches to a measurement of C centimetres. a) Write the function as an equation in 2 variables. C = 2.54 i b) Determine the value of C(12).What does this number represent? C(12) = 2.54 (12) = 30.48 ; this number represents "cm" if domain is 12 inches. c) Determine the value of i when C(i) = 100. What does this number represent? C(i) = 100 =2.54 i , i= 100 39.37 2.54 This number represents "in" if range is 100 cm. 10. A car is traveling toward Meadow Lake Park, Saskatchewan. The equation D = –80t + 300 represents the distance, D kilometres, to Meadow Lake after t hours of driving. a) Describe the function. Write this equation in function notation. D(t) = –80t + 300 b) How far away from Meadow Lake Park was the car at the start of its journey? How do you know? At the start of the journey, t = 0, if substitute 0 for t. D(0) = –80 (0) + 300 = 300 km 5 9 11. The function C(f ) = (f –32) converts a temperature, f degrees Fahrenheit, to C degrees Celsius. a) Determine: i) C(50) 5 9 C(50) = (50 –32) = 10° C ii) C(–13) 5 9 C(–13) = (–13 –32) = –25° C b) Determine each value of f when: i) C(f ) = 20 ii) C(f ) = –35 c) Write an equation in function notation to relate the temperatures in each fact. i) Pure water freezes at 0°C or 32°F. ii) Cookies are baked at 180°C or 356°F.