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The amplitude of the trigonometric function shown below is defined as the average of the absolute values of the maximum value of f(x) and the minimum value of f(x). The trigonometric function graphed below can be described by the equation f(x) = a sin(bx + c), where a, b, and c are real numbers. Which of the following values describes the amplitude of this function?

(A) 1

(B) 2

(C) 3

(D) π

(E) 2π

The Correct Answer
Explanation

If point A has a non-zero x-coordinate and a non-zero y-coordinate and at least one of these coordinate values is positive, then point A must be located in which of the 4 quadrants labeled below?

(A)I only (B) I or II only (C) II or IV only (D) II, III, or IV only (E) I, II, or IV only

Correct Answer: E

If a5 for a ≠ 0, which of the following statements must be true?

(F) x ≠ 0 and y ≠ 0 (G) x + y = 5 (H) x - y = 5 (J) xy = 5 (K) = 5

Correct Answer: H

If a(x) = b(x) + c(x), where b(x) = 3x2 - 8x + 113 and c(x) = - 3x2 + 18x + 7 and x is an integer, then a(x) is always divisible by which of the following?

(A) 6 (B) 7 (C) 10 (D) 12 (E) 15

Correct Answer: C

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