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Removing Discontinuities

AP Calculus AB· difficulty 2/5

The function f(x)=x2−9x−3f(x) = \dfrac{x^2 - 9}{x - 3} has what kind of discontinuity at x=3x = 3?

  • A

    Removable (hole)

    check_circle
  • B

    Jump

  • C

    None — it is continuous

  • D

    Infinite (asymptote)

Explanation

Factor: f(x)=(x−3)(x+3)/(x−3)=x+3f(x) = (x-3)(x+3)/(x-3) = x+3 for x≠3x \ne 3. The function has a removable hole at x=3x = 3, where it can be redefined as f(3)=6f(3) = 6.

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