Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)

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

y = -2 - cot (x - π/4)

Based on the answer in Exercise 58 and the fact that the cotangent function has period π, give the general form of the equations of the asymptotes of the graph of y = -2 - cot (x - π/4).

Let n represent any integer.

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 = cot (x/2 + 3π/4)

Identify the circular function that satisfies each description.

period is π; function is decreasing on the interval (0, π)

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