Question

A sinusoidal function has a frequency of 1/6π, 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

Given the frequency is 1/6π

A maximum value is 12

A minimum value is -6

A y-intercept is 3.

The general form of the sinusoidal function,

$f=a.\sin (bx+c)+d$

Given

$\begin{gathered} b=\frac{1}{3} \\ T=\frac{2\pi}{b} \\ T=\frac{2\pi}{\frac{1}{3}} \\ T=6\pi \end{gathered}$$\begin{gathered} f=\frac{1}{T} \\ f=\frac{1}{6\pi} \end{gathered}$

The maximum value is 12.

$9+3=12$

The minimum value is -6.

$-(9-3)=-6$

the y-intercept of 3.

$f(x)\text{ = }9\text{ sin(}\frac{1}{3}x)+3$

Thus, the given option (a) is correct.