Question

Help ASAP!!Using the graphed function above, find the following

Answer 1

Answer:

Maximum: 1, Minimum: -3, Midline y = -1, Amplitude = 4, Period = $\pi$, Frequency $\displaystyle =\frac{1}{\pi}$,  equation : $f(x)=-4cos(2x)+1$

Step-by-step explanation:

Sinusoid Functions

It refers to the oscillating functions like the sine or cosine which range from a minimum and maximum value periodically.

The graph shown can give us all the information we need to answer these questions:

Maximum: 1

Minimum: -3

The midline goes through the center value (mean) of the max and min values, i.e.

Equation of the midline:

$\displaystyle y=\frac{1-3}{2}=-1$

Amplitude is the difference between the maximum and minimum values

$A=1-(-3)=4$

The period is the time it takes to complete a cycle. We can see the minimum value is first reached at x=0 and next at $x=\pi$

Thus the period is

$T=\pi$

The frequency is the reciprocal of the period:

$\displaystyle f=\frac{1}{T}=\frac{1}{\pi}$

The angular frequency is

$\displaystyle w=2\pi f=\frac{2\pi }{\pi}=2$

The equation of the function is a negative cosine (since it starts at the minimum) or a shifted sine or cosine. We'll choose the negative cosine, knowing all the parameters:

$f(x)=-4cos(2x)+1$