Please help my homework on odd number questions also include explanations "EXCEPT" question 77-81

Use Theorem 1 to determine where each function in Problems 31-40 is continuous. 31. f(x) = 3x - 4 32. h(x) = 4 - 2x 3x 2x 33. g(x) = 34. k(x) = x + 2 x - 4 x+1 x - 2 35. m(x) = 2+ 3x - 4 36. n(x) =- x2 - 2x - 3 2x 1 - x2 37. F(x) = x2 + 9 38. G(x) x2 + 1 x2 + 4 39. M(x) = x - 40. N(x) = 4x2 - 9 4 - 25x2 In Problems 47-54, use a sign chart to solve each inequality. Express answers in inequality and interval notation. 47. x2 - x - 12 10x 50. x2 + 7x > - 10 51. x3 0 x2 + 5x . 53. > 0 54. x - 4 10x 50. x2 + 7x > - 10 69. f(x) = Itx ifx 0 15-x ifx21 53 * + 5x 0 54. x - 4 - 1 496 CHAPTER 9 Limits and the Derivative 71. f(x) = 1+ x ifxs 2 In Problems 77-82, discuss the validity of each statement. (5 - x ifx > 2 If the statement is always true, explain why. If not, give a counterexample. 72. f (x ) = x ifxs 2 (2x ifx > 2 77. A polynomial function is continuous for all real numbers. if x 0 79. If f is a function that is continuous at x = 0 and x = 2, then f is continuous at x = 1. if x 0 81. If f is a function that has no partition numbers in the interval