Maxine Lifshitz's Amsco's AP Calculus AB BC: Preparing for the Advanced PDF

By Maxine Lifshitz

ISBN-10: 1567655629

ISBN-13: 9781567655629

Presents an entire assessment of themes integrated within the university Board AP Calculus AB and Calculus BC direction descriptions and should support scholars boost the abilities and techniques had to prevail on either the Calculus AB and Calculus BC checks.

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C) Domain of the inverse of g(x) is the set of real numbers. Range of the inverse of g(x) is {y Ͼ 0}. 4 Inverses 29 Exercises Multiple-Choice Questions No calculator is allowed for these questions. 1. Which of the following graphs show(s) a function that has an inverse? y 4. The composition of a function f and its inverse is equal to (A) Ϫ1 (B) 0 (C) 1 (D) x (E) 1 x x I 3. The graphs of a function and its inverse are reflections of each other across (A) the x-axis (B) the y-axis (C) the origin (D) y ϭ x (E) y ϭ Ϫx y Free-Response Questions A graphing calculator is required for some questions.

Limits will be discussed next in Chapter 3. Multiple Representations of a Function The AP Calculus courses emphasize the importance of being able to represent a function in multiple ways. Students should be able to represent functions graphically, numerically, algebraically, and verbally. They should also be able to convert flexibly from one representation to another. Much of the power of calculus derives from being able to approach problems from different perspectives. Students who are skilled at representing functions in multiple ways are able to approach problemsolving situations from a variety of perspectives and can choose from a number of techniques and methods when working toward a solution.

B) Does f(x) have an inverse? Explain your answer and find the inverse if it exists. (c) Graph g(x) ϭ x3 Ϫ 1. (d) Does g(x) have an inverse? Explain your answer and find the inverse if it exists. Chapter Assessment 37 3. Copy the table below and fill in the domain, range, roots, symmetry, and asymptotes (if any) of each of the following functions. Then sketch the graph of each function without using a calculator Function Domain Range Roots Symmetry Asymptotes (a) y ϭ x2 (b) y ϭ ln x (c) y ϭ 2x (d) y ϭ sin x (e) y ϭ 0 x 0 38 Chapter 2 • Functions and Their Properties 4.

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Amsco's AP Calculus AB BC: Preparing for the Advanced Placement Exams by Maxine Lifshitz

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