--gf b o] 5 & o * e For Exercises 5 - 10, determine if the function is continuous at the given value of . If the function is not continuous at x = c, also state the condition in the definition of continuity at a point that fails first mathematically. 5. f()=32-4x+5, c=0 6. f(x)=-2-2-10, =2 x=2 1. fix)= y =2 T e e 5,9and 11 x=35 (x+3)(x=7) ) 9. fiy="2Nx=0) . _4 x=17 2x+3 10. = =2 0= -2 For Exercises 11 - 22, determine where the function is continuous algebraically. Write your answer using interval notation. 1. f(x)=4x>=Tx+3 12. f(x)=-Tx-x-1 x+1 3. - 13. f(x) e 2x+1 4. - 4. @) x+3 15, f()= 2x=THx-3) (x=3)(2x+3) 16. f(x) = (x+1)(3x-5) (3x -5)(7x- 1) 17. f (x) = Vx-7 18. f(x) = Vx+ 1 19. f(x ) = 23-x 20. f(x) = e7x-10 21. f(x) = log4 (2x -5) 18 and 21 22. f(x) = In(8-3x) INTERMEDIATE SKILLS PRACTICE For Exercises 23 - 26, use the graph of f to determine the x-value(s) where f is discontinuous. State the condition in the definition of continuity at a point that fails first at each x-value mathematically. ..... 23. -7 ... .... ..... 24.25. . .A... 26. For Exercises 27 - 34, determine if the function is continuous at the given value of c. If the function is not continuous at x = c, also state the condition in the definition of continuity at a point that fails first mathematically. 27. f(x) = *+ x-2 x2 - x-12' C=-2 28. f ( x ) = = 2x2 - x-3 x2 -6x-7' C =7 25,27 and 31 29. f (x) = 3x2 + 17x-28 2x2 - 17x+8 ' C= 8 30. f(x) = = 2x2 - x - 15 3x2 -2x- 16' , C= 10 4x+7 x52 31. f(x) = , C= 2 3x -5 x>2 3x2+9 *5-5 32. f (x) = C=-5 (x - 3)2+20 x>-54x3-11 x 8 17x3 +4x -10 x 5 2x2-4x+7 x3 X - 7 x-4 51 5x2 + 20x + 20 x6 -x -6 x50 52. f(x) = 2x2-4x-6 01 x2 -4 x2 +6x+8 *2 For Exercises 55 - 61, find the value(s) of k that make(s) the function continuous for all real numbers. If there is no such value of k, explain why. kx x 1 x5 5 58. f ( x ) = (212 - kx + 4 x>5 Sx xSk 59. f ( x ) = (2 x + 1 x > k 4x -3 x k 62. Find the value(s) of k that make(s) the following function continuous at x = -1. If there is no such value of k, explain why 12-kx x5-1 f (x) = 1 (x2 - 3x x>-1 TAMU 1491.4 Continuity from a Calculus Perspective 63. Find the value(s) of k that make(s) the following function continuous at x = 4. If there is no such value of k, explain why. f ( x ) = x - 8 x 8 MASTERY PRACTICE For Exercises 65 - 83, determine where the function is continuous algebraically. Write your answer using interval notation. 65. f(x) = _ In (7x-14) V2x + 10 66. f(x) = - In(x) - V21x+3 6.x2 + 23x - 18 67. f(x) = Vx2 -49 x2+36 ex/(x+3) 69 68. f(x) = Vx2 - 16 Vx + 5 69. f(x) = ; In(2-x) 70. f (x ) = - Vx+5 5 V2x+3 4 Vx+2 71. f(x) = 5 log(7x + 3) -10.(3) 2-3x 72. f(x) = x6 -25x4 73. f (x) = In(13 - x) Vx+4-3\f