Types of Discontinuities

AP Calculus · Axiom Academy

LESSON Types of Discontinuities Understand different ways functions can break Removable Discontinuity (Hole) A function has a removable discontinuity at x = a if: There's a hole in the graph at (a, L) But either f(a) is undefined or f(a) ≠ L A function has a jump discontinuity at x = a if: Left and right one-sided limits exist Example: The floor function has jumps at every integer. Infinite Discontinuity (Vertical Asymptote) A function has an infinite discontinuity at x = a if one or both one-sided limits approach ±∞: Example: has an infinite discontinuity at x = 0 A function has an oscillating discontinuity at x = a if it oscillates wildly as x approaches a. Example: oscillates infinitely as x approaches 0

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