Graph each function over a two-period interval.

y = -2 + (1/2) sin 3x

Graph each function over a two-period interval.

y = sin [2(x + π/4) ] + 1/2

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 1 + 2 sin ¼ x

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = -3 sin x

Determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin (1/2) x

Determine the amplitude and period of each function. Then graph one period of the function. y = -3 sin 2πx

In Exercises 53–60, use a vertical shift to graph one period of the function. y = sin x + 2

In Exercises 53–60, use a vertical shift to graph one period of the function. y = cos x + 3