changing the sine function

You need to find a solution of the form

A + B sin (Cx - D)

where A shifts the wave up, here A = 3 as the wave moves around +3

B gives the size up and down, if B = 1 we have a size of 2, so we want B = 3 as we have a size of 6

C controls the period, a normal wave is period 2 pi, we want period 6, so C = pi/3

D controls the shift to the right, we actually want the shift to the left so that Cx - D = 0 when x = -3 hence D = -pi

$\displaystyle

y = 3 + 3sin\left(\frac{\pi}{3}x + \pi\right)

$

hope this helps you do the second question on your own.

cheers

Nobby