Lesson 1 Answer Keys Winter 2015

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1 Lesson 1 s Winter 2015 Lesson 1 You-Try Problems 3. a) Input: Time (in years); Output Value: (in dollars) b) Dependent: V ; Independent: t c) Two years after purchase, the value of the car was $ d) Yes. Value of the car is a function of time. Each input is paired with a single output. 6. Functions: A, B, D, F, Not Functions: C, E 12. a) f(2) = -10, (2, -10) b) f( ) = 7, (, 7) 3 3 c) f(-3) = 5, (-3, 5) d) f(8/3) = -12. (8/3, -12) e) f(-x) = 3x 4 f) f(x 5) = -3x a) Domain:{7, 8, 11}, Range: {8, 12, 21} b) Domain: {3, 6, 8}, Range: {33, 42, 51} c) Domain: 7 x < 4, [ 7,4), Range: 6 f(x) < 7, [ 6,7) 22. a) C(x) = 3.25x b) 0 miles, 25miles c) $30, $ d) If 60 miles are towed, the cost is $225. e) (15, 78.75) If 15 miles are towed, the cost is $ f) x = 0 (0, 30) If 0 miles are towed, the cost is $ a) t = time in years b) V(t) = value in $ c) 1200, 600, 0 d) Graph should include labels for plotted points and axes. Points should be connected. Graph should not extend beyond the starting/ending points from the table. e) 8 years old f) $1000 g) 0 t 12 years or [0, 12] h) $ 0 Vt ( ) $1200 or [0, 1200] Lesson 1 Practice Problems 1.1: What is a function? Pages : a) time in minutes, t, distance in km, D b) {(0, 0), (20, 4003), (40, 9452), (60, 14232), (80, 18700), (100, 20200), (120, 20200)} c) Forty minutes after being launched, the satellite is 9452 km from the Earth d) Yes. Every time value has exactly one distance value. e) No. The distance value 20,200 km corresponds to two time values, 100 minutes and 120 minutes.

2 2: a) time in minutes, t, number of Gene copies, G b) {(0, 52), (3, 104), (5, 165), (6, 208), (8, 330), (10, 524), (12, 832)} c) After six minutes of observation, there are 208 gene copies. d) Yes. Every time value has exactly one number of Gene Copies value. e) Yes. Every number of gene copies has exactly one corresponding time value. 3: a) time in minutes, t, number of homework problems completed, H b) {(0, 0), (10, 3), (20, 8), (30, 8), (40, 15), (50, 17), (60, 20)} c) After forty minutes, Tara completed 15 homework problems. d) Yes. Every time value has exactly one corresponding number of homework problems completed. e) No. The number of homework problems completed value of 8 corresponds to two time values, 20 minutes and 30 minutes. 4: a) time in minutes, t, number of hotdogs eaten, H b) {(0, 0), (1, 8), (3, 23), (5, 37), (7, 50), (9, 63), (10, 68)} c) After seven minutes, the competitive hotdog eater had eaten 50 hotdogs. d) Yes. Every time value has exactly one corresponding number of hotdogs eaten e) Yes. Every number of hot dogs eaten has exactly one corresponding time value 1.2: Multiple representations of functions Pages : a) Yes b) Yes c) No d) Yes e) No 6: a) No b) Yes c) No d) Yes e) No f) Yes g) No 7: a) Yes b) Yes c) Yes d) No e) No f) No 8: Results Vary 9: a) Constant b) Decreasing c) Increasing d) Increasing e) Decreasing f) Constant 10: a) Increasing b) Decreasing c) Constant d) Constant e) Decreasing f) Increasing Section 1.3: Function Evaluation Pages : a) 4 b) 7 c) 6 12: a) 20 b) 6 c) 14 13: a) 18 b) 13 c) 4 14: a) 18 b) 4 c) 0

3 15: a) 2x + 6 b) 1 x + 6 c) x : a) 14 6t b) 14 1 t c) 6 2t 2 17: a) 8c 2 + 6c + 4 b) 2c 2 7c + 9 c) 2x 2 + 5x : a) Given: Input Finding: Output Ordered Pair: (2, 0) b) Given: Output Finding: Input Ordered Pair: (3, 3) c) Given: Input Finding: Output Ordered Pair: ( 4, 18) d) Given: Output Finding: Input Ordered Pair: ( 2, 12) 19: a) Given: Input Finding: Output Ordered Pair: (4, 11 2 ) b) Given: Output Finding: Input Ordered Pair: ( 7 3, 3) c) Given: Input Finding: Output Ordered Pair: ( 8, 25 2 ) d) Given: Output Finding: Input Ordered Pair: ( 2, 7 2 ) 20: a) 7 b) 7 c) 14 21: a) Given: Output Finding: Input Ordered Pair: (0, 12) b) Given: Input Finding: Output Ordered Pair: ( 4,3) c) Given: Output Finding: Input Ordered Pair: ( 4,3) d) Given: Input Finding: Output Ordered Pair: (2, 17) 22: a) Given: Output Finding: Input Ordered Pair: (0, 5) b) Given: Input Finding: Output Ordered Pair: ( 2,3) c) Given: Output Finding: Input Ordered Pair: ( 2,3) d) Given: Input Finding: Output Ordered Pair: (3,9) 23: a) Given: Output Finding: Input Ordered Pairs: (0, 5), (6,5) b) Given: Input Finding: Output Ordered Pair: (2, 3) c) Given: Output Finding: Input Ordered Pair: (1,0), (5,0) d) Given: Input Finding: Output Ordered Pair: (3, 4)

4 24. y 2x 3 a. b. x y f (x) 3x 4 a. b. x y Section 1.4: Domain and Range Pages : a) Domain: {3, 5, 7, 9, 11, 13} Range: { 2, 1, 8, 4} b) Domain: { 2, 1, 0, 1} Range: { 5} c) Domain: { 3, 1, 0, 4} Range: {2, 5, 3, 2} 27: a) Domain: { 10, 5, 0, 5, 10} Range: {3, 8, 12, 15, 18} b) Domain: { 20, 10, 0, 10, 20, 30} Range: { 4, 14, 32, 50, 68, 86} c) Domain: {1, 2, 3, 4, 8, 9, 10, 11, 12} Range: {54, 62, 66, 69, 72, 73, 74}

5 28: a) Domain: Inequality Notation < x <, Interval Notation (, ) Range: Inequality Notation < y <, Interval Notation (, ) b) Domain: Inequality Notation 8 x 6, Interval Notation [ 8, 6] Range: Inequality Notation 4 y 4, Interval Notation [ 4,4] c) Domain: Inequality Notation 6 x 7, Interval Notation [ 6, 7] Range: Inequality Notation 3 y 2, Interval Notation [ 3,2] d) Domain: Inequality Notation 8 < x 7, Interval Notation ( 8, 7] Range: Inequality Notation 5 y < 4, Interval Notation [ 5,4) Section 1.5: Applications of Functions Pages : a) C(w) = 0.50w + 20 b) 0 w 200 c) 20 C(w) 120 d) w C(w) e) C(50) = 45. When 50 windows are washed, the total cost is $45. f) C(50) = 45. When 50 windows are washed, the total cost is $45. g) Solve 45 = 0.50w + 20 for w. 30: a) b) (0,0) or P(0) = 0, (8,96)or P(8) = 96 c) Input Quantity: time in hours Practical Domain: Inequality Notation 0 t 8, Interval Notation [0, 8] d) Output Quantity: number of pizzas made

6 Practical Domain: Inequality Notation 0 P(t) 96, Interval Notation [0, 96] e) P(3) = 36. The number of pizzas made in 3 hours is 36. f) P (5 5 6 ) = 70. Seventy pizzas are made in hours or 5 hrs and 50 minutes. 31: a) x is used for the input b) The number of years since 1900 c) L is used for the output d) The life expectancy for males in years e) x L(x) f) Practical Domain: 0 x 120 g) Practical Range: 48.3 L(x) 80.7 h) L(43.3) = , so the man was born in 1943.

7 Section 1.1: What is a Function? Media Example 1, workbook page 11

8 Section 1.2: Multiple Representations of Functions Media Example 4, workbook page 14

9 Media Example 7, workbook page 16

10 Section 1.3: Function Notation Media Example 9, workbook page 18

11 Media Example 11, workbook page 19

12 Media Example 13, workbook page 21

13 Media Example 14, workbook page 21

14 Media Example 15, workbook page 22

15 Media Example 16, workbook page 23

16 Section 1.4: Domain and Range Media Example 17, workbook page 24

17 Section 1.5: Applications of Functions Media Example 20, workbook page 26