What occurs when applying a vertical shift to a graph of a function?

When a vertical shift is applied to the graph of a function, the entire graph moves either up or down by a fixed amount. This adjustment affects all points on the graph equally, meaning that every point's y-coordinate is increased or decreased by the same value.

For example, if you take a function f(x) and apply a vertical shift by adding a constant k, creating a new function f(x) + k, the graph of this new function will be the same shape as the original but displaced vertically. If k is positive, the graph will move upwards; if k is negative, it will move downwards.

This characteristic distinguishes vertical shifts from other transformations such as horizontal shifts, stretches, or reflections, which have different effects on the orientation or shape of the graph.