Consider the following function from Example 5. Work these exercises in order.

y = -2 - cot (x - π/4)

Use the fact that the period of this function is π to find the next positive x-intercept. Round to the nearest hundredth.

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

y = tan 3x

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

y = 1/3 tan (3x - π/3)

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

y = cot (x/2 + 3π/4)

Match each function in Column I with the appropriate description in Column II.

I

y = -4 sin(3x - 2)

II

A. amplitude = 2, period = π/2, phase shift = ¾

B. amplitude = 3, period = π, phase shift = 2

C. amplitude = 4, period = 2π/3, phase shift = ⅔

D. amplitude = 2, period = 2π/3, phase shift = 4⁄3

In Exercises 17–24, graph two periods of the given cotangent function. y = 2 cot x

In Exercises 17–24, graph two periods of the given cotangent function. y = 1/2 cot 2x

In Exercises 18–24, graph two full periods of the given tangent or cotangent function. y = −2 tan π/4 x