Vertical Shifts : ## y=f(x) +h## where the graph shifts ##k## units up if ##k## is positive and downwards when ##k## is negative.

Horizontal Shifts : ##y=f(x+h)## where the graph shifts to the left by ##h## units when positive and to the right when ##h## is negative.

2.Upon shift the coordinate axes :

##x=X+h## encapsulates the x-coordinate of any point w.r.t original axes (##x##), the coordinate of the point w.r.t 'new' axes (##X##) and the x-coordinate of the new origin w.r.t original axes (##h##). Likewise for the y-coordinate we have ##y=Y+k##.

3.I understand that shifting the axes to the left is the equivalent of shifting the graph of a function to the right.

My Question : Given the above points, I believe there should be some sort of correlation between the two sets of formulas(?).

My Guess : Since ##y=f(x+h)## where shifts the function to the left, this ought to be the same as ##y=f(X)## where ##X=x+h##, yet this does not conform to the derived formula. (Maybe I am making an error by not clearly labelling each variable?)