Chapter 2 Radical Functions Assignment

Transcription

1 Chapter Radical Functions Assignment Name: Short Answer 1. Determine the equation of each radical function, which has been transformed from b the given translations. a) vertical stretch b a factor of 5, then a horizontal translation of 6 units right b) horizontal stretch b a factor of, then a vertical translation of units down c) horizontal reflection in the -axis, then a vertical translation of 9 units up and horizontal translation of units right d) horizontal stretch b a factor of, vertical reflection in the x-axis, and vertical stretch b a factor of. For each graph, write the equation of a radical function of the form. a) x

2 b) x c) x 3. Determine the domain and range of each function. a) b) c)

3 . a) Sketch the graph of each function, and then sketch the graph of. b) State the domain and range of each f(x) and g(x). i) ii) iii)

4 5. Using each graph of, sketch the graph of. a) x 3 5 b) x 3 5 c) x 3 5

5 6. Sketch the graph of and use it to sketch the graph of. 7. Solve the equation,, algebraicall. 8. Solve the equation using technolog.

6 9. A student designs a special container as part of an egg drop experiment. She believes that the container can withstand a fall as long as the speed of the container does not exceed 80 ft/s. She uses the equation to model the velocit, v, in feet per second, as a function of constant acceleration, a, in feet per second squared and the drop distance, d, in feet. The acceleration due to gravit is 3 ft/s. a)assuming the student s specifications are correct, will the egg break if the student drops the egg from shoulder height (5 ft) off a building 80 ft high? b)what is the maximum height the egg can be dropped from? 10. Solve the equation graphicall using technolog. 11. Solve the equation algebraicall.

7 Problem 1. The speed, s, in metres per second, of sound in dr air is can be described b the function, where T is temperature, in degrees Celsius. a) Determine the domain and range of the function. b) Determine the speed of sound, to the nearest tenth of a metre per second, for each of the following temperatures. i) 8 C ii) 1 C iii) 3 C c) Graph the function using technolog and determine the x-intercept. d) What is the meaning of the x-intercept in this context?. The manufacturer of a new Global Positioning Satellite (GPS) sstem wants to predict the consumer interest in its new device. The compan uses the function to model the number, I, in thousands, of pre-orders for the GPS as a function of the number, w, of weeks before the GPS release date. a) What are the domain and range and what do the mean in this situation?

8 b) Identif the transformations represented b the function compared to. c) Graph the function and explain what the shape of the graph indicates about the situation. d) Determine the number of pre-orders the manufacturer can expect to have 10 weeks before the release date.

9 3.Consider the function. a) Determine the square root of the function. b) Graph the functions on the same set of axes. c) State the domains and ranges of the graphs. d) Describe the relationship between the domain and range of f(x) and the domain and range of g(x).

10 . The kinetic energ (energ of motion), E, in joules, of an object is given b the equation, where m represents the mass of the object, in kilograms, and v represents its speed, in metres per second. a) Determine the general equation for the velocit of a mass as a function of its kinetic energ. b) Find the speed of an object of mass 1 kg moving with a kinetic energ of i) 00 J ii) 0 J c) Graph the function if the mass is 1 kg. d) John conducts an experiment and graphs the data, resulting in the graph below. What is the mass of the object? x

11 Chapter Radical Functions Assignment Answer Section SHORT ANSWER 1. ANS: Substitute values into the general equation. a) b) c) d) PTS: 1 DIF: Average OBJ: Section.1 NAT: RF13 TOP: Radical Functions and Transformations KEY: transformations. ANS: a) b) c) PTS: 1 DIF: Average OBJ: Section.1 NAT: RF13 TOP: Radical Functions and Transformations KEY: graph transformations 3. ANS: a) b) c) PTS: 1 DIF: Average OBJ: Section.1 NAT: RF13 TOP: Radical Functions and Transformations KEY: domain range. ANS: a) i) The graph of is shown in blue and the graph of is shown in red.

12 x ii) The graph of is shown in blue and the graph of is shown in red. x iii) The graph of is shown in blue and the graph of is shown in red. x b) i) ii) iii) PTS: 1 DIF: Average OBJ: Section. NAT: RF13 TOP: Square Root of a Function KEY: graph domain range square root of a function 5. ANS: The graph of is shown in black, and the graph of is shown in blue.

13 a) x 3 5 b) x 3 5 c) x 3 5 PTS: 1 DIF: Average OBJ: Section. NAT: RF13 TOP: Square Root of a Function KEY: graph square root of a function 6. ANS: The graph of = f(x) is shown in black, and the graph of is shown in blue.

14 x 3 5 PTS: 1 DIF: Difficult OBJ: Section. NAT: RF13 TOP: Square Root of a Function KEY: graph square root of a function 7. ANS: PTS: 1 DIF: Average OBJ: Section.3 NAT: RF13 TOP: Solving Radical Equations Graphicall KEY: algebraic solution 8. ANS: (50, 1) x PTS: 1 DIF: Average OBJ: Section.3 NAT: RF13 TOP: Solving Radical Equations Graphicall KEY: graphical solution

15 9. ANS: The velocit can be calculated b using the height from which the egg is dropped. The height is 80 ft plus the height of the student, or 85 ft. Since the speed is less than 80 ft/s, the egg will not crack. The maximum height is limited b a velocit of 80 ft/s, so The maximum height is 100 ft. PTS: 1 DIF: Average OBJ: Section.3 NAT: RF13 TOP: Solving Radical Equations Graphicall KEY: algebraic solution 10. ANS: (, ) x PTS: 1 DIF: Difficult OBJ: Section.3 NAT: RF13 TOP: Solving Radical Equations Graphicall KEY: graphical solution 11. ANS:

16 PTS: 1 DIF: Difficult OBJ: Section.3 NAT: RF13 TOP: Solving Radical Equations Graphicall KEY: algebraic solution PROBLEM 1. ANS: a) Domain: Range: b) i) ii) iii) c) s ( 73.15, 0) T The x-intercept is d) The x-intercept is the temperature when the speed of sound is 0.

17 PTS: 1 DIF: Average OBJ: Section.1 Section.3 NAT: RF13 TOP: Radical Functions and Transformations Solving Radical Equations Graphicall KEY: x-intercepts domain range. ANS: a) Since I 0, solve to find the lower boundar of the domain. The upper boundar of the domain is the value of x at the vertex,. So the domain is and the range is. The domain is negative, indicating the weeks remaining before the launch of the GPS. The maximum number of GPS units expected to be pre-ordered is 15 thousand. b) a = 3: reflection in the x-axis with a vertical stretch b a factor of 3 b = 1: reflection in the -axis h = 1: translation of 1 unit left k = 15: vertical translation up 15 units c) x 6 The number of pre-orders increases as the GPS release date gets closer. Since w is negative, it represents the number of weeks remaining before release. The function s maximum of 15 thousand is the maximum number of pre-orders

18 d) Six thousand pre-orders can be expected 10 weeks before the release date. PTS: 1 DIF: Difficult OBJ: Section.1 NAT: RF13 TOP: Radical Functions and Transformations KEY: translations graph domain range 3. ANS: a) b) g(x) f(x) x c) The domain of f(x) is and the domain of g(x) is. The range of f(x) is and the range of g(x) is. d) The domain of g(x) consists of all values of the domain of f(x) where f(x) 0. The range of g(x) consists of the square root of all positive values of the range of f(x). PTS: 1 DIF: Difficult OBJ: Section.3 NAT: RF13 TOP: Solving Radical Equations Graphicall KEY: graph square root of a function domain range. ANS: a) b) i) Substitute m = 1 and E = 00 in the equation.

19 The speed of the object is 5.8 m/s. ii) Substitute m = 1 and E = 0 in the equation. The speed of the object is 8. m/s. c) When m = 1, 10 v E d) The point (0, ) is on the graph. Substitute this into the equation and solve for m.

20 The mass of the object is 10 kg. PTS: 1 DIF: Average OBJ: Section.1 NAT: RF13 TOP: Radical Functions and Transformations KEY: graph horizontal stretch