Horizontal Shifts

These are quite simple as well though there is one bit where we have to be careful.

Given the graph of f ( x ) the graph of g ( x ) = f ( x + c ) will be the graph of f ( x ) shifted left through c units if c is +ve and or right by c units if c is -ve.

Now, we have to be careful here. A +ve c shifts a graph in the negative direction and a negative c shifts a graph in the +ve direction. They are precisely opposite than vertical shifts and it's simple to flip these around & shift wrongly if we aren't being careful.