In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = sin(x − π)

Key Concepts

Amplitude

Amplitude refers to the maximum height of a wave from its midline. In the context of the sine function, it indicates how far the graph reaches above and below the horizontal axis. For the function y = sin(x - π), the amplitude is 1, as the coefficient of the sine function is 1, meaning the graph oscillates between 1 and -1.

Period

The period of a trigonometric function is the length of one complete cycle of the wave. For the sine function, the standard period is 2π. In the given function y = sin(x - π), there is no coefficient affecting the x variable, so the period remains 2π, indicating that the function will repeat its values every 2π units along the x-axis.

Phase Shift

Phase shift refers to the horizontal displacement of a periodic function. It is determined by the value subtracted from the variable inside the function. In y = sin(x - π), the phase shift is π units to the right, as the function is shifted from the standard position of sin(x) to the right by π, affecting where the wave starts on the x-axis.