Does the Graph move Left or Right?

Sometimes the easiest things are the hardest to remember! For example, if you have the graph of y = sin(x) and you add "a" to x, does the graph of

y = sin(x + a) move to the left or right of the graph of sin x?

Here is an easy way to work it out: think about what happens if x = 0! If

x = 0 then the graph of y = sin(x) is 0 (the red line), but the graph of

y = sin(x + pi/6) (the blue line) is sin (pi/6); not 0. It is where the other graph was when x = pi/6, so the original graph has moved to the left. Positive values for a move it left, negative values move it right.