Question

A sinusoidal function has a frequency of 3, a maximum value of 12, a minimum value of -6 and a y-intercept of 3. Which Function could be the function described

Answer 1

The sinusoidal function that can be described is:

• $f(x) = 9\sin{(6\pi x)} + 3$

What is a sinusoidal function?

A sinusoidal function is a trigonometric function, and has the following format, considering no phase shift:

$y = A\sin{Bx} + C$

In which:

• 2A is the amplitude, which is the difference between the largest and smallest value.

• The period is $\frac{2\pi}{B}$, hence the frequency is $\frac{B}{2\pi}$.

• C is the vertical shift.

In this problem, the maximum value is of 12, a minimum value of -6, hence:

$2A = 18$

$A = \frac{18}{2} = 9$

Frequency of 3, hence:

$\frac{B}{2\pi} = 3$

$B = 6\pi$

With no vertical shift, the function would have minimum at -9 and maximum of 9, it has a maximum value of 12 and a minimum value of -9, hence the vertical shift is of C = 3.

Then, the function is:

$f(x) = 9\sin{(6\pi x)} + 3$

You can learn more about sinusoidal functions at https://brainly.com/question/26315885