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\fHD . 1080 s occur naturally in SECTION 2.2 Elementary Functions: Graphs and Transformations 65 ple 1 to compute In Problems 11-26, graph each of the functions using the graphs 39. 40. ewise definition of functions f and g below. as and graph the f (x ) 8 (x) 41. 12. gas in one 11 . y = f (x ) + 2 12 . y = 8 (x ) - 1 13 . y = f (x + 2 ) 14 . y = 8 (x - 1 ) 15 . y = 8 (x - 3 ) 16. y = f (x + 3 ) - 5 repre- 17 . y = 8 (x ) - 3 resents the 18 . y = f (x ) + 3 19. y = -f(x ) 20. y = -8(x) 21. y = 0.58 (x) 22. y = 2f(x) 23. y = 2f (x ) + 1 24. y = -0.58(x) +3 In Problems 43-48, the graph of the function g is formed by 25. y = 2(f(x) + 1) 26. y = - (0.58(x) + 3) applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using B In Problems 27-34, describe how the graph of each function is -5 5 x 5 5 and-5= y=5. se equa- related to the graph of one of the six basic functions in Figure I on page 58. Sketch a graph of each function. 43. The graph of f(x) = Vx is shifted 2 units to the right and 3 units down. 27 . 8 (x ) =- 1x+ 31 28. h (x ) = - |x - 51 44. The graph of f(x) = Vx is shifted 3 units to the left and 29. f(x ) = (x - 4) 2 - 3 30. m ( x ) = ( x + 3 ) 2 + 4 2 units up. 31. f(x) = 7 - Vx 32. 8 (x ) = -6 + Vx 45. The graph of f(x) = [x| is reflected in the x axis and shifted 33. h(x) = -31x1 to the left 3 units. 34. m(x) =-0.4x2 46. The graph of f( x) = [x| is reflected in the x axis and shifted rma Each graph in Problems 35-42 is the result of applying a se- to the right 1 unit. indi- quence of transformations to the graph of one of the six basic functions in Figure I on page 58. Identify the basic function and 47. The graph of f(x) = x' is reflected in the x axis and shifted describe the transformation verbally. Write an equation for the 2 units to the right and down 1 unit. given graph. 48. The graph of f(x) = x2 is reflected in the x axis and shifted m- to the left 2 units and up 4 units. 35. 36. ise Graph each function in Problems 49-54. 49 . f ( x ) = 2 - 2x ifx 10 52 . h (x ) = 10 + 2x if0 5 x = 20 40 + 0.5x ifx> 20 2 x if 0 S x = 20 53 . h (x ) = x + 20 if 20 40