Question

1. what is the amplitude of this sinusoidal function? a. 3 b. 2π c. 6 d. -3

Explanation:

Step1: Recall Amplitude Definition

Amplitude of a sinusoidal function \( y = A\sin(Bx - C) + D \) (or cosine) is the absolute value of \( A \), representing the distance from the midline to the peak (or trough).

Step2: Analyze the Graph

The midline here is \( y = 0 \) (x - axis). The peak (or trough) is at \( y = 3 \) (or \( y = - 3 \)). The distance from midline (\( y = 0 \)) to peak (\( y = 3 \)) is \( |3 - 0| = 3 \). Amplitude is positive (magnitude), so it's 3. Options B (\( 2\pi \)) is period - related, C (6) would be total distance from peak to trough, D (-3) is invalid as amplitude is non - negative.

Answer:

A. 3