4. Graphing Trigonometric Functions

In Exercises 1–6, 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

Graph y = 1/2 sin x + cos x, 0 ≤ x ≤ 2π.

In Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function.y = 3 sin 1/2 x

In Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function.y = -3 sin 2πx

In Exercises 12–13, use a vertical shift to graph one period of the function.y = 2 cos 1/3 x − 2

In Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function.y = -sin 2/3 x

In Exercises 14–15, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π.y = sin x + cos 1/2 x

Graph each function. See Examples 1 and 2.ƒ(x) = 3|x|

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)

Graph each function. See Examples 1 and 2.ƒ(x) = ⅔ |x|

Graph each function. See Examples 1 and 2.g(x) = 2x²

In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function.y = 3 sin(2x − π)

Graph each function. See Examples 1 and 2.g(x) = ½ x²

In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function.y = 1/2 sin(x + π/2)

Graph each function. See Examples 1 and 2.ƒ(x) = -½ x²