4. Graphing Trigonometric Functions

Graph each function over a two-period interval. See Example 4.

y = -3 + 2 sin x

Graph each function over a two-period interval. See Example 4.

y = -1 - 2 cos 5x

Graph each function over a two-period interval.

y = 1 - 2 cos ((1/2)x)

Graph each function over a two-period interval.

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

Graph each function over a two-period interval.

y = -3 + 2 sin (x + π/2)

Fill in the blank(s) to correctly complete each sentence.

The graph of y = -5 + 2 cos x is obtained by shifting the graph of y = 2 cos x ________ unit(s) __________ (up/down).

Graph each function over a two-period interval.

y = sin [2(x + π/4) ] + 1/2

Fill in the blank(s) to correctly complete each sentence.

The graph of y = 3 + 5 cos (x + π/5) is obtained by shifting the graph of y = cos x horizontally ________ unit(s) to the __________, (right/left) stretching it vertically by a factor of ________, and then shifting it vertically ________ unit(s) __________. (up/down)

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

y = 2 sin 5x

Fill in the blank(s) to correctly complete each sentence.

The graph of y = -2 + 3 cos (x - π/6) is obtained by shifting the graph of y = cos x horizontally ________ unit(s) to the __________, (right/left) stretching it vertically by a factor of ________, and then shifting it vertically ________ unit(s) __________. (up/down)

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

y = 1 + 2 sin ¼ x