AP Calculus AB: Continuity — Drill 1

About This Drill

AP Calculus AB: Continuity — Drill 1 is a Math practice drill covering Limits and Continuity. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice the three-part definition of continuity, identify types of discontinuities, and determine whether a function is continuous at a point or on an interval. These AP Calculus AB skills appear on both the multiple-choice and free-response sections.

Questions in This Drill

1. Which of the following conditions is NOT required for a function \( f \) to be continuous at \( x = a \)?
2. The function \( f(x) = \dfrac{x^2 - 9}{x - 3} \) has what type of discontinuity at \( x = 3 \)?
3. Let \( f \) be defined by \( f(x) = x^2 + 1 \) for \( x < 2 \) and \( f(x) = kx - 1 \) for \( x \geq 2 \). For what value of \( k \) is \( f \) continuous at \( x = 2 \)?
4. A student claims: “If \( \lim_{x \to 4} f(x) = 7 \), then \( f \) must be continuous at \( x = 4 \).” Which of the following best explains why this claim is incorrect?
5. Let \( f \) be defined by \( f(x) = \dfrac{x^2 - 4}{x - 2} \) for \( x \neq 2 \) and \( f(2) = 5 \). Which of the following statements about \( f \) is true?