Question

In: 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) = 1/4 sin x

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

f(x) = 1/4 sin 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)

Sine function:

A sine function is a trigonometric function representing ratio between opposite side to hypotenuse. It is an odd function with period 2π.

A general form of sine function is

y = Asin(Bx – C) + D

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

In this case the sine function is

f(x) = 1/4sinx

Comparing with the general form the amplitude is

|A| = 1/4

Period of the function is

P = 2π/|B|

= 2π

Since, D = 0, the midline equation is

y = 0

There are no asymptotes.

Amplitude of the function is 1/4.

Period of the function is 2π.

Mid line of the function is y = 0.

Graph is plotted as follows:

Junaid answered 1 year ago

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) = 2tan(x − π/6)

For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.f(x) = 2tan(x − π/6)

For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.

For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline. f(x) = −cos (x + π/3) +1

For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = −cos (x + π/3) +1

For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline. f(x) = πcos(3x + π)

For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = πcos(3x + π)

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

For the following exercises, determine the amplitude, period, and midline of the graph, and then find a formula for the function.

For the following exercises, determine the amplitude, period, and midline of the graph, and then find a formula for the function.Give in terms of a sine function.

For the following exercises, graph two full periods of each function and state the amplitude, period, and midline...y = 2sin(3x − 21) + 4

For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.y = 2sin(3x − 21) + 4

For the following exercises, graph two full periods of each function and state the amplitude, .... y = 3sin(8(x + 4)) + 5

For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.y = 3sin(8(x + 4)) + 5

For f(x)=x^2+x-2/x^2-4, determine the equation for any vertical asymptotes, the equation for any horizontal asymptotes, and...

For f(x)=x^2+x-2/x^2-4, determine the equation for any vertical asymptotes, the equation for any horizontal asymptotes, and the x-coordinates of any holes