12 15 The graph of f (x) is shown in the figure at the -2 2 3 4 6 -5 -1 0 - 3 - 2 2 8 11 9 h (x ) 6 8. Let g (x) = -2f(xx +1). Sketch Selected values of the function h(x) are shown in the table above. Use the values in the table to answer the following 4. Let h(x) = 6f(x+2) -3. (a) Find f(4). (b) Find f(0). (c) If f ( k ) = 2, find k. 5. Let h(x) =-29 (2) (a) Find g (6). (b) If g(x) = 1, find x. (c) Put the following in order from least to greatest: g(-1), g(1), g(2). 6. Let h(x) be the function that results from applying three transformations to the graph of j in this order: (a) Find j (6). a horizontal dilation by a factor of 5, a vertical dilation by a factor of 2, and a vertical translation by - 4 units. (b) Find j(-3). 7. Let w(x) = 2h(x - 3) + 1 (a) Find w(-2) . h(6). (b) Find w(h(-5)). (c) Find w(w(2) ). Worksheet: (Topic 1.12) Transformations of Functions Created by Bryan PasswaterE - (2 "(0) / pula (9) 21 9 4 8 2 1- 2- IT 8 2 2- &- 0 1 action h (x ) are shown in the table above, Use the values in the table to answer the following. (c ) 1ff( k ) = 2 , find k. The graph of f(x) is shown in the figure at the right and consists of three line segments. 8. Let g(x) = -2f(x + 1). Sketch the graph of g(x). 9. Let h(x) = f(2x) - 3. Sketch the graph of h(x). The graph of f (x) is shown above and has the domain [-3, 5] and the range [-1, 3]. 10. Let k (x) = -3f(2x) + 1. 11. Let p(x) = =f(x+ 3) - 4. Find the domain and range of k (x). Find the domain and range of p(x). Worksheet: (Topic 1.12) Transformations of Functions Created by Bryan Passwater12. The graph of f(x) has zeros at x = -2, 0, and 3. Find the zeros of the following functions. (a) g(x) = 2f(x -4) ( b ) h ( x ) = - 3f ( 2 x ) (c ) k (x ) =-5f(3x - 2) 13. The graph of f (x) has the vertical asymptote x = -2 and horizontal asymptote y = 3. Find the vertical and horizontal asymptotes of the following functions. (a) g(x) = 2f(x+1)-3 (b) h (x) = 4 - 3f (5) ( c ) k ( x ) = =f(4 - 2x ) + 3 14. Let f(x) = x2 + 4x + 1. Write an equation of the following functions that are transformations of f (x). (a) g(x) = 3f(x)-7 b) k(x) = f(x- 2) (c) p(x) = 2f(x+1)-5 (d) s(x) = -f(-x) Worksheet: (Topic 1.12) Transformations of Functions Created by Bryan Passwater