Math

posted by .

Describe the intervals on which the following function is continuous. If not continuous, state "where" the discontinuity occurs and state the TYPE of discontinuity.
f(x)= (x^2-x-12)/(x^2-6x+8)

I just don't understand how to find the intervals. Thanks~

  • Math -

    f(x)= (x^2-x-12)/(x^2-6x+8)
    = (x-4)(x+3)/( (x-2)(x-4)
    = (x+3)/(x-2) , x not= 4

    So the function is discontinuous at x=4 and at x = 2
    with a "hole" at (4, 7/2)
    and a vertical asymptote at x = 2

    So continuous for

    x<2 OR x > 2, x not= 4

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus please help!

    Which of the following functions f has a removable discontinuity at a?
  2. Calculus

    A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x)=2x^2+3x–14/x–2 …
  3. Calculus

    A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x)=2x^2+3x–14/x–2 …
  4. Calculus

    A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. -------------------------------------------------------------------------------- …
  5. Calculus

    A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. -------------------------------------------------------------------------------- …
  6. Calculus

    Suppose g(x) = { 1 / (x - 2) if x < 1 2x - 4 if x >/= 1 The best description concerning the continuity of g(x) is that the function A.) is continuous B.) has a jump discontinuity C.) has an infinite discontinuity D.) has a removable …
  7. Calculus - #1

    Suppose g(x)={1/x+1 if x<1 {2x-1 if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. has …
  8. Calculus - #2

    Suppose g(x)={x^2+2x+1/x+1 if x<1 {2x if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. …
  9. Calculus - #3

    Suppose g(x)={1/(x-2) if x<1 {2x-3 if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. …
  10. Calculus - #4

    Suppose g(x)={1/(x-2) if x<1 {2x-4 if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. …

More Similar Questions