Vertical Translation

Question

Find an equation for a sine function having an amplitude of 3, period of 4pi, horizontal shift of 2pi to the left, and a vertical shift of 1.

Answer 1

Start with amplitude.

Y = 3sin(x)

Now period

Y = 3sin(2pix/4pi) = 3sin(x/2)

Now horizontal shift

Y = 3sin( (x+2pi)/2 )

Now the vertical shift

Y = 3sin( (x+2pi)/2 ) + 1