continuity, discontinuities and the Intermediate Value Theorem

Review continuity, discontinuities and the Intermediate Value Theorem for AP Calculus AB and try 2 free AP-style practice questions. 61 questions on this topic in AP Calculus AB · Unit 1 · Limits and Continuity.

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Question 1

Let $f$ be defined by $f(x) = \dfrac{x - 3}{x - 3}$ for $x \neq 3$ , and $f$ is not defined at $x = 3$ . Which of the following conditions for continuity at $x = 3$ fails?

Question 2

The function $f$ is defined by $f(x) = x^2 + k$ for $x \le 4$ and $f(x) = 2x + 7$ for $x > 4$ . For what value of $k$ is $f$ continuous at $x = 4$ ?

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Full practice for AP Calculus AB · Unit 1 · Limits and Continuity: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.

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Answer, then see why

The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?

Not quite. The answer is B.

Why the other options are wrong

AI grading for free-response

Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.

Question 13 / 4 pts

Part a1 / 1 pts

Point 1: Earned

94% sure

Reason: Correctly identifies demand for gasoline as inelastic.

Evidence: "The price of gasoline rises and the quantity falls only a little."

Part b2 / 3 pts

Point 1: Earned

91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned

88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned

82% sure

Reason: With inelastic demand, a price increase raises total revenue.

Evidence: "Revenue goes down."

Continuity, discontinuities and the Intermediate Value Theorem: AP Calculus AB Practice Questions | S&D Academy