Mathematics 30-1: Unit 3 Lesson A - Assignment Booklet Multiple-Choice Items _________ 1. The transformation of y = f(x) to y = f(2x) is a 1 2 A. horizontal stretch factor of 1 2 B. horizontal stretch factor of 2 C. vertical stretch factor of 1 2 D. vertical stretch factor of 2 2. The function y = -3f(x) can be described as a reflection in the A. x-axis with a horizontal stretch factor of 3 B. y-axis with a vertical stretch factor of 3 C x-axis with a vertical stretch factor of 3 D. y-axis with a horizontal stretch factor of 3 Numeric Response 1 1 If the point (1, 3) lies on y = f(x), then the y coordinate of the corresponding point on the transformed function y = 2f(4x) is Lesson A - Assignment Booklet 3 3. The point A(4, -6) is a point on y = f(x). The coordinate pair of point A mapped onto y = 2f(x - 3) + 1 is 2 Mathematics 30-1: Unit 3 A. (1, -10) B. (7, -11) C. (7, -10) D. (1, -11) 1 4. The function y = f(x) is stretched horizontally by a factor of 2 and stretched vertically by a factor of 3. Then, it is reflected in the x-axis and translated 4 units to the left. The transformed function can be written as A. y = 3f(2x + 4) B. y = 2f(3x + 12) C. y = -2f(3x + 4) D. y = -3f(2x + 8) Numeric Response 2 2 The vertex of f(x) = |x| is (0,0) and the vertex of y = -4f(5(x - 3)) + 7 is (h, k), then h is 1 5. Select the statement of inverse relations that is false. A. the range of a function will be the domain of its inverse B. the inverse of a function will always be a function C. inverse relations are reflections in the line y = x D. the domain of a function will be the range of its inverse Mathematics 30-1: Unit 3 2 Lesson A - Assignment Booklet 6. Select the inverse of f(x) = x2 + 9, x < 0, x d R. A. x = y2 + 9 y = x- 9 B. f -1 ^ x h = - x - 9 , x 2 9 C. f -1 ^ x h = x - 9 , y 1 0 D. Numeric Response 3 1 If y = f(x) has a y-intercept of 3 and an x-intercept of 4, then y = f-1(x) has an x-intercept of 1 7. The translation of a function may change A.\tthe shape and position of the graph B. neither shape nor position of the graph C.\tthe shape but not position of the graph D.\tthe position but not the shape of the graph Written Response 1. The graph of f(x) = (x - 2)2 is transformed to y = f(x + 5) - 4. 2 Determine the vertex of y = f(x) and the vertex of the transformed function. 2 The point (6,16) lies on y = f(x). Determine the corresponding point on the transformed function. 1 The point (-9, 0) lies on the transformed function. What is the corresponding point on the original function y = f(x)? Lesson A - Assignment Booklet 2. Mathematics 30-1: Unit 3 The graph of y = f(x) is shown below. 9 y 8 7 6 5 4 3 y = f(x) 2 1 -4 -3 -2 -1 -0 1 2 3 4 x 2 Determine the domain and range of y = f(x). 1 On the same grid above, sketch y = 2f(-x). 2 Determine the domain and range of y = 2f(-x). 3. The graph of f(x) = x2 has been transformed so that it now has a vertex of (4,-1), opens down, and was stretched so that it passes through the point (5, -3). Sketch both parabolas on the grid provided. 2 Mathematics 30-1: Unit 3 2 Lesson A - Assignment Booklet Determine the equation of the transformed function. 2 In words, describe the transformations that have occurred from the graph of y = f(x) to the transformed graph. Lesson A - Assignment Booklet Mathematics 30-1: Unit 3 Mathematics 30-1: Unit 3 2 2 Lesson B - Assignment Booklet 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 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 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. 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 . Lesson B: Transforming Functions Mathematics 30-1: Unit 3