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=(1)/(3) \\ T=(2\pi)/(b) \\ T=(2\pi)/((1)/(3)) \\ T=6\pi \end{gathered}`
`\begin{gathered} f=(1)/(T) \\ f=(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(}(1)/(3)x)+3`

Thus, the given option (a) is correct.