AP Calculus ABmediummcq1 pt

Which of the following statements is true about the function f(x) = 1/x²?

A.C) The function is continuous on the entire real line.
B.A) The function has an infinite discontinuity at x = 0.
C.D) The function has no discontinuities.
D.B) The function has a removable discontinuity at x = 0.

Explanation

Core Concept

The function f(x) = 1/x² has an infinite discontinuity at x = 0 because as x approaches 0, the function approaches ∞. This is the primary reason the function has an infinite discontinuity at x = 0. Option A is correct because the function has an infinite discontinuity at x = 0. Option B is incorrect because the discontinuity is not removable. Option C is incorrect because the function is not continuous at x = 0. Option D is incorrect because the function has an infinite discontinuity.

Correct Answer

BA) The function has an infinite discontinuity at x = 0.

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