What intervals is the function continuous on according to the document?

The document indicates that the function is continuous on the open interval (–2, –1) and (0, 1). The continuity of the function is crucial for applying the Intermediate Value Theorem effectively.

What values of c make the function continuous at x = 3?

The document states that for the function to be continuous at x = 3, the value of c must be 6. This is determined by ensuring that the limits from both sides of the function at x = 3 are equal to the function's value at that point.

What does the Intermediate Value Theorem guarantee in the document?

According to the document, the Intermediate Value Theorem guarantees a solution to the equation f(x) = –2.998 on the closed interval [1, 2]. This theorem is fundamental in calculus as it ensures that if a function is continuous on an interval, it takes on every value between f(a) and f(b) for some point in the interval.

Which statements about horizontal and vertical asymptotes are true?

The document discusses that the function has a horizontal asymptote at y = 0 because as x approaches infinity, f(x) approaches 0. Additionally, it mentions that the graph has a vertical asymptote at x = 5, indicating that the function approaches infinity as x approaches this value.

What is the significance of the function's continuity on specific intervals?

The document emphasizes that the function is continuous on the interval [–1, 3) and not continuous on the interval (–1, 3). This distinction is important for understanding the behavior of the function and for applying calculus concepts such as limits and derivatives effectively.

How does the document define the function g(x)?

The document defines the function g(x) as g(x) = x + tan(x) – 10. This definition is essential for analyzing the function's properties, including its continuity and potential asymptotic behavior.

What does the document say about the behavior of the function at x = 2?

At x = 2, the document indicates that the function approaches a specific value, which is critical for determining continuity and the existence of limits at that point. Understanding this behavior helps in graphing the function accurately.

AP Calculus AB Unit 1 Progress Check MCQ Solutions PDF

AP Calculus AB Unit 1 Progress Check focuses on multiple-choice questions that assess students' understanding of calculus concepts. This resource provides answers to various questions related to continuity, the Intermediate Value Theorem, and function behavior. Ideal for AP Calculus students preparing for exams, it covers essential topics and problem-solving strategies. The document includes detailed explanations for each question, helping students grasp complex calculus principles effectively.

Key Points