AP Calculus ABmediummcq1 pt
The function f(x) = 1/x has a discontinuity at x = 0 due to
A.A hole in the graph at x = 0
B.A jump in the graph at x = 0
C.A vertical asymptote at x = 0
D.A horizontal asymptote at x = 0
Explanation
Core Concept
The function f(x) = 1/x has a vertical asymptote at x = 0 since the function approaches ∞ as x approaches 0 from the right and approaches negative ∞ as x approaches 0 from the left. This is the primary reason why the function is discontinuous at x = 0. Options A and B are incorrect since the function does not have a hole or a jump at x = 0. Option D is incorrect since the function approaches ∞ and negative ∞ as x approaches 0, not a horizontal asymptote.
Correct Answer
CA vertical asymptote at x = 0
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