Question

PLEASE HELP :( i'm stuck

What are the amplitude and midline?

Amplitude: 1; midline: y = 1
Amplitude: 0; midline: y = 0
Amplitude: 2; midline: y = 1
Amplitude: 2; midline: y = 0

Answer 1

Amplituide is and midline is y = 1.

Answer 2

Amplitude: 1; midline: y = 1

Explanation:

From the graph we can conclude that it is a sine or cosine function. In their standard form, these functions are given by the following equations:

`y(t)=Acos(\omega t +\phi)\\\\or\\\\y(t)=Asin(\omega t+ \phi)`

Where:

`A=Amplitude=(|A_m_i_n-A_m_a_x|)/(2)\\\omega=Angular\hspace{3}frequency\\\phi=Initial \hspace{3}phase`

And:

`A_m_a_x=Maximum\hspace{3}amplitude\\A_m_i_n=Minimum\hspace{3}amplitude`

On the other hand, we can define the midline of these kind of functions as the halfway between the maximum and minimum amplitude of the function, Therefore:

`Midline=M_l=(A_m_a_x+A_m_i_n)/(2)`

From the graph you can see that the maximum value of the function(maximum amplitude) is 2 and the minimum value of the function (minimum amplitude) is 0, thus:

`A=(|A_m_i_n-A_m_a_x|)/(2) =(|0-2|)/(2) =(|-2|)/(2) =(2)/(2) =1`

And:

`M_l=(A_m_a_x+A_m_i_n)/(2)=(2+0)/(2) =(2)/(2) =1`