Question

Write the particular equation of this transformed sine graph. Assume that the horizontal shift is 1 unit to the right. pic attached

Answer 1

Since, you asked too many questions from this,

See, when a function y=f(x) is shifted vertically, it changes to y+k = f(x) .. [ k is positive when shifted downward by k units and negative when shifted upwards by k units]

when a graph of y= f(x) is shifted horizontally, it changes to y= f(x+k) [ k>0 for leftward shift by k units and k<0 for rightward shift]

And as far as finding the center of the sinusoidal curve is concerned,

See that this is a sinusoidal curve, y= Sin x which is shifted, two units up and half units right..

Now use above info to find your resulting equation..