Question

For the function "y = sin(1/3 * x - 4)", what values represent its amplitude, period, and horizontal shift?

a) Amplitude: 1/3, Period: 4, Horizontal Shift: -4
b) Amplitude: 1, Period: 3, Horizontal Shift: 4
c) Amplitude: 4, Period: 1/3, Horizontal Shift: -4
d) Amplitude: 3, Period: 1, Horizontal Shift: 4

Answer 1

The amplitude of the wave is 1, the period is 3, and the horizontal shift is 4. Hence, option B is correct.

Step-by-step explanation:

The function y = sin(1/3 * x - 4) represents a sinusoidal wave. The amplitude of the wave is the maximum value it reaches, which is determined by the coefficient in front of the sine function. In this case, the coefficient is 1, so the amplitude is 1. The period of the wave is the distance between two consecutive points on the wave with the same value. The coefficient in front of the x in the sine function determines the period, and in this case, it is 3. Therefore, the period is 3.

The horizontal shift of the wave is determined by the constant term in the sine function. In this case, it is 4, which means the wave is shifted 4 units to the right on the x-axis. So, the horizontal shift is 4.