Question

In: Advanced Math

For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. f(x) = 0.2cos(0.1x) + 0.3

For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.

f(x) = 0.2cos(0.1x) + 0.3

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)

Cosine function:

A cosine function is a trigonometric function representing ratio between adjacent side to hypotenuse. It is an even function with period 2π.

A general form of cosine function is

y = Acos(Bx – C) + D

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

Consider the following trigonometric expression:

f(x) = 0.2cos(0.1x) + 0.3

Comparing with the general form the amplitude is

|A| = 0.2

Period of the function is

P = 2π/|B|

= 2π/0.1

= 20π

Since, D = 0.3, the midline equation is

y = 0.3

There are no asymptotes.

Amplitude of the function is 0.2.

Period of the function is 2π/.01.

Mid line of the function is y = 0.3.

Graph is plotted as follows:

Junaid answered 1 year ago

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