Why does the translation y=f(x+2) translate the graph f(x) 2 units left instead of 2 to the right?
It seems like f(x+2) should translate the graph y=f(x) 2 to the right, it is +2 inside the bracket after all? However, if we think of the translation as actually subbing in x+2 into the equation y=f(x), it may become more intuitive. For example, take f(x)=x2, this will give f(x+2)=(x+2)2. Look at when x2=0 and when (x+2)2=0. This will happen at x=0 and x=-2 respectively. Subsequently, the point (0,0) from (x,f(x)) has become (-2,0) in (x,f(x+2)). This means it has been moved 2 to the left. More generally, if we thing of any point on the graph y=f(x), the translation of f(x+2) will take values of f(x) that are 2 to the right of it. This will make y=f(x+2) 2 units left of the y=f(x).
