By Maxine Lifshitz
Presents an entire evaluate of issues integrated within the university Board AP Calculus AB and Calculus BC path descriptions and should support scholars advance the abilities and methods 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
When the graph of a function is shifted or flipped, the rule for the function changes, though the graph remains essentially the same. Rules for Translating and Reflecting Functions • If a function f(x) is translated to the right c units, its new equation is f(x Ϫ c). • If a function f(x) is translated to the left c units, its new equation is f(x ϩ c). • If a function f(x) is translated down c units, its new equation is f(x) Ϫ c. • If a function f(x) is translated up c units, its new equation is f(x) ϩ c.
F(2) ϭ (A) 0 (B) 1 (C) 2 (D) 4 (E) does not exist 0 1 2 4 does not exist 0 1 2 e does not exist (a) Find the value of k so that f(x) is continuous at x ϭ 1. (b) Using the value of k found in part (a), sketch the graph of f(x). x2 ϩ 2, x Ͻ Ϫ1 2. g(x) ϭ e x Ϫ p, x Ն Ϫ1 4. lim f(x) ϭ x→2 0 1 2 4 does not exist 5. f(1) ϭ (A) 0 (B) 1 (C) 2 (D) e (E) does not exist 0 1 2 e does not exist Free-Response Questions No calculator is allowed for these questions kx ϩ 1, x Ͻ 1 1. f(x) ϭ e 2 x Ն 1 x, x→2 For Exercises 5–8, use f(x) ϭ e (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) 0 1 2 4 does not exist 3.
A) y ϭ 2x ϩ 3 (B) y ϭ 2x (C) y ϭ x2 (D) y ϭ "x (E) y ϭ 0 x 0 Free-Response Questions A graphing calculator is required for some questions. 1. (a) Sketch the graph of each function below by hand. f(x) ϭ x4 Ϫ x3 g(x) ϭ ln x h(x) ϭ x Ϫ 1 (b) Graph the 3 functions in the calculator and use q Box centered at (1, 0). (c) Write a sentence that describes the relationship between f(x), g(x), and h(x) for values of x near (1, 0). (d) Find the range of f(x). ) 2. (a) Graph f(x) ϭ x3 Ϫ x. (b) Does f(x) have an inverse?
Amsco's AP Calculus AB BC: Preparing for the Advanced Placement Exams by Maxine Lifshitz