Alberta Distance Learning Centre MAT3791 Math 30-1 Unit 3: Transformations Lesson B: Transforming Radical, Sinusoidal, Exponential, and Rational Functions Student's Questions and Comments For Student use only For ADlC USE ONLY (If label is missing or incorrect) Assigned to File Number: Marked by Name Address Province Postal Code Apply Assignment Label Here City/Town Please use the correct preprinted label for this course and Assignment Booklet. Mark:\t% Date Received: Summary Total Weighting Practice SelfAssessment 20% Assignment 80% Blended Booklet Grade Teacher's Comments Teacher's Signature NEW SEPT 2012 Your Marks Mathematics 30-1: Unit 3 Lesson B - Assignment Booklet Back to Baker Street... Complete the Back to Baker Street assignment. Refer to the Tips from Scotland Yard located at the back of this lesson booklet to assist you in completing the assignment. Please show pertinent work and explanations. Call or e-mail your teacher if you would like additional help. Multiple-Choice Items 2 2 1. The transformations that affect the domain of the function y = x are A. horizontal translation and horizontal stretch B. horizontal stretch, horizontal translation, and reflection in the y-axis C. horizontal translation and reflection in the y-axis D. horizontal stretch and reflection in the y-axis 2. The function f (x) = x which has been transformed to y = -2f(-x + 3) + 1, results in the mapping of (4, 2) to A. (-7, -3) B. (-1, -3) C (-5, -3) D.\t(-11,-3) Numeric Response 1 3 The function y = x is stretched vertically by a factor of a and is translated 3 units to the right and 4 units down. If this transformed function passes through the point (5, 2). then the value of a, to the nearest hundredth, is Alberta Distance Learning Centre 93 Lesson B - Assignment Booklet 2 3. The range of the function f(x) = -2 cos(3(x - )) + 4 is 1 Mathematics 30-1: Unit 3 A. 2 f(x) 6 B. 6 f(x) < 10 C. -10 f(x) -6 D. -6 f(x) -2 4. The horizontal asymptote of y = 3(2)4(x - 1) + 5 is A. y = 5 B. y=3 C. x=1 D. y = 0 Numeric Response 2 4 2 The function y = x is stretched horizontally by a factor of 2 and vertically by a factor of 3; it is then translated 4 units up and 6 units to the left. If this transformed function is g(x), then, to the nearest hundredth, g(10) = 3 5. The horizontal and vertical asymptotes of y = ^ - h - 5 are x 2 2 A. horizontal asymptote is at x = -2, vertical asymptote is at y = 5 B. horizontal asymptote is at x = 2, vertical asymptote is at y = -5 C. horizontal asymptote is at y = 5, vertical asymptote is at x = -2 D. horizontal asymptote is at y = -5, vertical asymptote is at x = 2 6. The domain of y = 5f(2x + 4) + 3 where f(x) = 1 is x A. x 0 B. x -4 C. x -2 D. x -3 94 Alberta Distance Learning Centre Mathematics 30-1: Unit 3 Lesson B - Assignment Booklet Numeric Response 3 4 A sinusoidal function, y = a sinb(x - c) + d has a maximum point at ` r , 3 j and a 4 minimum point at `- r , - 1 j . The values, in this order, of a, b, c, and d are 4 Written Response 1. The function y = a b ^ x - hh + k is shown in the graph below. 3 Determine the equation of this function if there is a vertical stretch factor and no horizontal stretch factor. 1 Determine the domain and range of this function. 1 Determine the equation of this function is there is a horizontal stretch factor and no vertical stretch factor. Alberta Distance Learning Centre 95 Lesson B - Assignment Booklet Mathematics 30-1: Unit 3 2. A sinusoidal function passes through (0,2), has a maximum point at (20, 5), and a minimum point at (60,-1) . 3 Determine the amplitude, period, and range of this function. 3 Determine a possible sine function with these characteristics. 3 Determine a possible cosine function with these same characteristics . Total: 96 36 Alberta Distance Learning Centre Lesson B: Transforming Functions Mathematics 30-1: Unit 3 S Standard of Excellence Students need to make connections to other courses to complete. Successful completion shows an ability to think beyond given examples. O Over the acceptable level of understanding Students need to make connections from within the course notes and example to complete. Successful completion shows an ability to draw from given instruction and apply skills to new problems. L Level of acceptable standards Students need to show an acceptable level of understanding to complete. Successful completion shows an ability follow given examples. V Below level of acceptable standards Student's response to question is below acceptable standard. E Inadequate level of acceptable standard Student's response to question indicates student needs assistance in understanding basic concepts. Thinkstock Alberta Distance Learning Centre 97