What transformation does the equation y = f(x) ± a represent?

The equation ( y = f(x) \pm a ) signifies a vertical transformation of the function ( f(x) ). When ( a ) is added to ( f(x) ) (i.e., ( y = f(x) + a )), the entire graph of the function shifts upward by ( a ) units. Conversely, when ( a ) is subtracted from ( f(x) ) (i.e., ( y = f(x) - a )), the graph moves downward by ( a ) units.

This type of transformation affects the y-values of the function directly, without altering the x-values, hence the movement is strictly vertical along the y-axis. The graph maintains its shape and orientation; it simply translates up or down depending on whether ( a ) is positive or negative. This concept is vital in understanding how functions can be manipulated graphically.