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Additional info for Calculus: A Complete Course (7th Edition)

Sample text

52. What is the effect on the graph of an equation in x and y of replacing x with x and y with y simultaneously? 53. Sketch the graph of |x| + |y| = 1. 4 down 1, right 1 x Find the points of intersection of the pairs of curves in Exercises 39 42. 43. y = x2 23 Functions and Their Graphs The area of a circle depends on its radius. The temperature at which water boils depends on the altitude above sea level. The interest paid on a cash investment depends on the length of time for which the investment is made.

F (x) = 1 g(x) = x, x g, 1 g(x) = 1+x Sketch the graphs of the functions in Exercises 3 6 by combining the graphs of simpler functions from which they are built up. x2 3. x 4. x 3 f g(0) f (g(x)) f f ( 5) f ( f (x)) (b) (d) (f) (h) 19. 2 f (x) 20. 21. f (2x) 22. f (x/3) 23. 1 + f ( x/2) g( f (0)) g f (x) g(g(2)) g g(x) 24. 2 f ((x y y = f (x) 2 8. f (x) = 2/x, g(x) = x/(1 x) 9. f (x) = 1/(1 x), g(x) = x 1 10. f (x) = (x + 1)/(x 1), g(x) = sgn (x) In Exercises 25 26, sketch the graphs of the given functions.

F (x) = 1 2 x) (1, 1) Sketch the graphs of the functions in Exercises 23 38. 2 f (1 2 19. f (x) = |x | , 1) 1 3 23. f (x) = 46. 1 y 1 16. f (x) = x +4 2 17. f (x) = x 2 43. 45. f (4 1 x2 42. f (x 1 49. f (x) = x 4 3 50. f (x) = 2 6x 3 + 9x 2 1 2x + x 2 2x + x 2 * 11. f (x) = x 2 + 1 41. f (x + 2) 33 x 1 2x 2 + 3x 52. f (x) = 2 x 2 x + 4x + 5 53. What function f (x), de ned on the real line , is both even and odd? 51. f (x) = Combining Functions to Make New Functions Functions can be combined in a variety of ways to produce new functions.