I think it's the third option, but i'm not sure please assist

Can't be sin function because it starts at zero at the origin (and there is no L-R shift in any of the answers)

Cos funtion starts at 1 at the origin....multiplying it by 7 stretches it up and down by 7   adding 3 shifts it up 3

    so your answer looks good to me  

The period has pi in it, so the answer can't be A or D. We know that (0, 10) is on the graph because the y-intercept is 10. Plug this into both of them to get 3 = 10 and 10 = 10. The one that is true is 10 = 10, which corresponds to \(\boxed{C}\).