Question

In: Advanced Math

For the following exercises, graph two full periods. Identify the period, the phase shift, the amplitude, and asymptotes. f(x) = 3cot x

For the following exercises, graph two full periods. Identify the period, the phase shift, the amplitude, and asymptotes.

f(x) = 3cot x

Expert Solution

Periodic function:

A periodic function is a function that repeats its value over a fixed interval. The fixed interval is called as period of the function. Mathematically it is represented as

f(x + P) = f(x)

Where P is the period of the function f(x)

Cot function:

A cot function is a trigonometric function representing ratio between adjacent sides to opposite side. It is an even function with period 2π.

A general form of cot function is

y = Asec(Bx – C) + D

Consider the following trigonometric function:

f(x) = 3cotx

Comparing with the general form the stretching factor is

|A| = 3

Period of the function is

P = π/|B|

= π

Since, D = 0, the midline equation is

y = 0

Asymptotes are at

0, π

Asymptotes of the function are 0 and π.

Amplitude of the function is 3.

Period of the function is π.

Mid line of the function is y = 0.

Graph is plotted as follows:

Junaid answered 1 year ago

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