4. Graphing Trigonometric Functions

In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π.y = 3 cos x + sin x

In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π.y = cos x + cos 2x

Graph each function. See Examples 6–8.g(x) = |x| - 1

In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π.y = cos x + sin 2x

Graph each function. See Examples 6–8.h(x) = -(x + 1)³

In Exercises 67–68, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 4.y = cos πx + sin π/2 x

Graph each function. See Examples 6–8.h(x) = 2x² - 1

Graph each function. See Examples 6–8.ƒ(x) = 2(x - 2)² - 4

Graph each function. See Examples 6–8.ƒ(x) = √x + 2

Graph each function. See Examples 6–8.ƒ(x) = √-x

Graph each function. See Examples 6–8. _ƒ(x) = 2√x + 1

Graph each function. See Examples 6–8.g(x) = ½ x³ - 4

In Exercises 79–82, graph f, g, and h in the same rectangular coordinate system for 0 ≤ x ≤ 2π. Obtain the graph of h by adding or subtracting the corresponding y-coordinates on the graphs of f and g.f(x) = 2 cos x, g(x) = cos 2x, h(x) = (f + g)(x)

In Exercises 79–82, graph f, g, and h in the same rectangular coordinate system for 0 ≤ x ≤ 2π. Obtain the graph of h by adding or subtracting the corresponding y-coordinates on the graphs of f and g.f(x) = cos x, g(x) = sin 2x, h(x) = (f − g)(x)

In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function.y = −2 sin(2πx + 4π)