Amsco's AP Calculus AB BC: Preparing for the Advanced - download pdf or read online

By Maxine Lifshitz

ISBN-10: 1567655629

ISBN-13: 9781567655629

Offers a whole overview of subject matters integrated within the university Board AP Calculus AB and Calculus BC direction descriptions and should support scholars enhance the abilities and techniques had to prevail on either the Calculus AB and Calculus BC checks.

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

Example text

Find the equations of the vertical asymptote(s) of y ϭ Solution The solutions are x ϭ 1 and x ϭ Ϫ1. Since neither of these values makes the numerator zero, both x ϭ 1 and x ϭ Ϫ1 are equations of vertical asymptotes. Zeros The zeros, or roots, of a function f(x) are the x-values such that f(x) ϭ 0. Some zeros are found by factoring. Other zeros may be approximated on a calculator. In some cases, such as complex roots, the roots do not appear on the calculator, but can sometimes be found by algebraic methods.

The domain of a function is the set of its x-coordinates. The x-coordinate is called the independent variable. Often the easiest way to find the domain of a function is to locate the values of x for which the function is not defined. In a rational function, for example, the function is not defined at those values of x for which the denominator is zero. The domain of a function is the set of x-values excluding those for which the 22 Chapter 2 • Functions and Their Properties function is not defined.

Which of the following is an even function with domain ϭ {reals}? (A) ln x2 (B) ex2 Ϫ x (C) ex2 Ϫ x2 (D) ex3 ϩ 1 (E) 2 1 x Ϫ4 4. Find the domain of f(x) ϭ ln(tan x) on the interval 3Ϫ␲, ␲ 4 . (A) all x in (Ϫ␲, ␲) (B) all x in (0, ␲) ␲ (C) all x in Q0, R 2 ␲ ␲ (D) all x in QϪ␲, Ϫ R and Q0, R 2 2 ␲ ␲ (E) all x in BϪ , R 2 2 (x Ϫ 1)2 has x2 Ϫ 1 a hole at x ϭ Ϫ1 holes at x ϭ Ϫ1 and x ϭ 1 vertical asymptotes at x ϭ 1 and x ϭ Ϫ1 a horizontal asymptote at y ϭ Ϫ1 a hole at x ϭ 1 and a vertical asymptote at x ϭ Ϫ1 5.

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


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