What does the transformation y = f(x ± a) do to the graph of the function?

The transformation represented by the equation y = f(x ± a) impacts the graph of the function by shifting it horizontally. When you see the equation with a plus sign (y = f(x + a)), it indicates that the graph will move to the left by 'a' units. Conversely, if there is a minus sign (y = f(x - a)), the graph shifts to the right by 'a' units.

This horizontal shifting occurs without altering the shape of the graph or its position on the vertical axis, which distinguishes it from transformations that would move the graph up or down (which would involve changing y values rather than x values). Therefore, the correct interpretation of this transformation is that it translates the graph left or right based on the value of 'a' in the context of the equation.