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) = 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)

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)

Tangent function:

A tan function is a trigonometric function representing ratio between opposite side to base. It is an odd function with period π.

A general form of tan function is

y = Atan(Bx – C) + D

In this case the tan function is

f(x) = 2tan(x – π/6)

Comparing with the general form the stretching factor is

|A| = 2

Period of the function is

P = π/|B|

= π

Since, D = 0, the midline equation is

y = 0

The asymptotes occur at

x = π/2|B| + π/|B|k

= π/2 and 3π/2

Asymptotes of the function are π/2 and 3π/2.

Amplitude of the function is 2.

Period of the function is π.

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) = 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

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, 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.

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