What would happen if you decrease 'k' in a rational function?

Decreasing 'k' in a rational function typically refers to a change in the vertical translation of the function. When 'k' is a constant added to or subtracted from the function, it affects the vertical position of the entire graph.

For instance, consider a rational function in the form ( f(x) = \frac{1}{x} + k ). If you decrease 'k' by moving it to a smaller value, this results in all y-values of the function shifting downward. Each point on the graph of the function will move down by the same amount as 'k' is decreased.

This downward movement occurs because for any given x-value, the function now outputs a lower y-value. Thus, the overall effect of decreasing 'k' is to translate the graph of the function downward in the coordinate plane.