AP Calculus AB 1.10 Exploring Types of Discontinuities Question Bank

Practise AP Calculus AB 1.10 questions by connecting piecewise formulas, graph features and limit behaviour to discontinuity types.

Exam points

distinguish holes, jumps and vertical asymptotes using limits and function values
locate and count discontinuities in piecewise and trigonometric functions

[Maximum number: 1]

Let f be the function given by $f(x)=\frac{x-2}{2|x-2|}$ . Which of the following is true?

$\lim _{x \rightarrow 2} f(x)=\frac{1}{2}$

f has a removable discontinuity at x=2.

f has a jump discontinuity at x=2.

f has a discontinuity due to a vertical asymptote at x=2.

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