By Maxine Lifshitz

Presents a whole overview of themes incorporated within the university Board AP Calculus AB and Calculus BC direction descriptions and may support scholars increase the talents and methods had to be successful on either the Calculus AB and Calculus BC tests.

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**Extra info for Amsco's AP Calculus AB BC: Preparing for the Advanced Placement Exams**

**Sample text**

The real zero(s) of f(x) ϭ x3 ϩ 2x2 ϩ 9x ϩ 18 are (A) Ϫ2 only (B) Ϫ3, Ϫ2 (C) ; 3, Ϫ2 (D) ; 3, ;2 (E) none 20. If f(x) ϭ x2 Ϫ 2x, then f(2 ϩ h) ϭ (A) h2 ϩ 4h ϩ 3 (B) h2 ϩ 8h ϩ 3 (C) h2 ϩ 2h ϩ 3 (D) h2 Ϫ 2h ϩ 3 (E) h2 ϩ 2h xϪ3 21. The domain of f(x) ϭ is "x Ϫ 2 (A) x Ն 2 (B) x Ͼ 2 (C) x Ͼ 3 (D) x Ͼ 2 and x 3 (E) x Ͻ 2 22. The range of y ϭ 2 0 x Ϫ 2 0 Ϫ 2 in the interval [0, 5] is (A) {0 Յ y Յ 5} (B) {2 Յ y Յ 5} (C) {Ϫ2 Յ y Յ 5} (D) {Ϫ2 Յ y Յ 4} (E) {0 Յ y Յ 4} 23. Which of the following has an inverse?

A) Give an example of an odd function which has x ϭ 0 in the domain and which passes through the origin. (b) Use the definition of an odd function to prove that the conditions in part (a) are true for all odd functions. CHAPTER 3 Limits and Continuity Introduction Understanding the concept of limit is central to understanding calculus. A limit is a value that a function approaches as x approaches some fixed value. The definition of the derivative of a function and the concept of an integral both involve a limiting process.

For example, if the graph of y ϭ x2 is moved 5 units to the right, the new rule is y ϭ (x Ϫ 5)2. If the graph is moved down 3 units, the new rule is y ϭ x2 Ϫ 3. If the graph is reflected across the x-axis, the new rule is y ϭ Ϫx2. When the graph of a parabola is shifted or reflected, the graph remains a parabola with properties similar to those of the original graph. If the graph of y ϭ ln x is shifted to the left 2 units, the new rule will be y ϭ ln(x ϩ 2). Practice in graphing both by hand and using a graphing calculator makes it easier to recognize that a group of functions can be understood as one function that has been shifted and/or reflected.