Question

A sine function has the following key features:

Period = 12

Amplitude = 4

Midline: y = 1

y-intercept: (0, 1)

The function is not a reflection of its parent function over the x-axis.

How would this graph look??

Answer 1

Hence the function is given by:

`y=4\sin ((\pi x)/(6))+1`

Explanation:

Let the general function be given by:

`y=a\sin (bx)+c`

As we know that period of
`\sin x` is
`2\pi`.

Hence for period to be 12 we have to consider the function as:

`\sin ((\pi x)/(6))`

Hence
`b=(\pi)/(6)`

Also the midline is y=1. this means that the minimum and maximum value are at the same distance from y=1.

also the amplitude of the function is 4.

i.e. the maximum value of the function is 4+1=5.

and the minimum value is -4+1=-3

Also y-intercept is (0,1) i.e. when x=0 y takes the value as 1.

i.e. c=1.

Hence the function is given by:

`y=4\sin ((\pi x)/(6))+1`