AP Precalculus Unit 3 Part B Passwater's MCQ Exam Review

The function g is defined by g(x) = a*sin(b*(x+c))+d, for constants a, b, c, and d. In the xy-plane, the points (3, -1) and (7, 3) represent a minimum value and a maximum value, respectively, on the graph of g. What are the values of a and d?

• a = 2 and d = -1

• a = 2 and d = 1

• a = 4 and d = -1

• a = 4 and d = 1

The function h is defined by h(x) = a*sin(b*(x+c))+d, for constants a, b, c, and d. In the xy-plane, the points (2, 4) and (4, 10) represent a minimum value and a maximum value, respectively, on the graph of h. What is the value of b?

• b = 2

• b = 4

• b = π/2

• b = π

The function f is defined by f(x) = a*cos(b*(x+c))+d, for constants a, b, c, and d. In the xy-plane, the points (π, 6) and (2π, 2) represent a maximum value and a minimum value, respectively, on the graph of f. What are the values of b and d?

• b = 2π and d = 2

• b = 1 and d = 2

• b = 2π and d = 4

• b = 1 and d = 4

The function k is defined by k(x) = a*cos(b*(x+c))+d, for constants a, b, c, and d. In the xy-plane, the points (π/4, 10) and (3π/4, 40) represent a minimum value and a maximum value, respectively, on the graph of k. What are the period and amplitude of the function k?

• The period is π/2 and the amplitude is 15.

• The period is π/2 and the amplitude is 30.

• The period is π and the amplitude is 15.

• The period is π and the amplitude is 30.

The function f is given by f(x) = 1 + 2 tan x. Which of the following gives the vertical asymptotes of f?

• pi/2 + pi k, where k is an integer

• pi/2 + 2pi k, where k is an integer

• pi/4 + pi/2 k, where k is an integer

• pi + 2pi k, where k is an integer

The function k is given by k(x) = tan(1/2 x). Which of the following gives the vertical asymptotes of k?

• pi/4 + pi/2 k, where k is an integer

• pi/2 + pi k, where k is an integer

• pi + 2pi k, where k is an integer

• pi + 4pi k, where k is an integer

The function g is given by g(x) = tan(pi x). Which of the following gives the vertical asymptotes of g?

• pi/2 + pi k, where k is an integer

• pi + 2pi k, where k is an integer

• 1 + pi/2 k, where k is an integer

• 1 + 2pi k, where k is an integer

The function h is given by h(x) = tan(x - pi). Which of the following gives the vertical asymptotes of h?

• pi/2 + pi k, where k is an integer

• pi/2 + 2pi k, where k is an integer

• pi k, where k is an integer

• 2pi k, where k is an integer

The graph of the function f is given in the xy-plane. If f(x) = a tan(bx), where a and b are constants, which of the following is true?

• (A) a > 0 and b > 1

• (B) a > 0 and b < 1

• (C) a < 0 and b > 1

• (D) a < 0 and b < 1

The graph of the function h is given in the xy-plane. If h(x) = tan(b(x + c)), where b and c are constants, what are the values of b and c?

• (A) b = 1 and c = -π/2

• (B) b = 1 and c = π

• (C) b = 2 and c = -π/2

• (D) b = 2 and c = π