Worksheet A: Continuity Name: Directions: Find and classify any x value(s) where the functions below have a discontinuity. Show all work. x- - 4 1. f (x) = = x2 - 5x + 6 2. g(x) = - x - 2x - 3x x2 - 3x - 4 x* - 4x2 3. Let & be the function defined by k(x) = x2 - 4x . Which of the following statements is true? A) k has a discontinuity due to a vertical asymptote at x = 0 and at x = 4. B) k has a removable discontinuity at x = 0 and a jump discontinuity at x = 4. C) k has a removable discontinuity at x = 0 and a discontinuity due to a vertical asymptote at x = 4. D) & is continuous at x = 0 and has a discontinuity due to a vertical asymptote at at x = 4. x3 - 9x 4. Let g be the function defined by 9(*) = x2 - x - 6 . Which of the following statements about g at x = -2 and x = 3 is true? A) g has a jump discontinuity at x = -2, and g is continuous at x = 3. B) g has a jump discontinuity at x = -2 and a removable discontinuity at x = 3. C) g has a discontinuity due to a vertical asymptote at x = -2, and g is continuous at x = 3. D) g has a discontinuity due to a vertical asymptote at x = -2, and g has a removable discontinuity at x = 3. f(x) U 12 3 5. The graph of f(x) is shown above. What are all the values of x for which f has a removable discontinuity? A) 1 only B) 5 only C) 1 and 7 only D) 1,5, and 7g(x) 3 -2 -1 0 3 6 6. The graph of g(x) is shown above. For which value(s) of * does g have a removable discontinuity? A) 0 only B) 2 only C) 0 and 4 only D) 0, 2, and 4 x2 - 6x+5 7. The graph of k(x) is shown above. Let h be the function defined by h(x) = 2 _ 4x + 3. . For which value(s) of x do the functions h and & both have a nonremovable discontinuity? x2 + 2, * 0 9. Let h be the piecewise defined function shown above. Find and classify any x values where h(x) is discontinuous. x3 - 1 k(x) = (x3 - 3x -4' * 3 11. Let f be the piecewise defined function shown above and let c be a positive constant. Find the value of c such that f (x ) has a hole at x = 3.x'+3, x=1 f ( x) = 17-3x, x21 12. The piecewise function f(x) is given above. Is f (x) continuous at x = 1? Give a reason for your answer. 9(x) = [2 cos(x) -3, x0 13. The piecewise function g(x) is given above. Is g(x) continuous at x = 0? Give a reason for your answer. h(x)=tax