vertical shift

A vertical shift slides an entire graph straight up or down without changing its shape. Picture lifting a drawing off the page and setting it back a few centimeters higher: every point moves the same amount, and the curve keeps its exact form.

You do this by adding a constant to the whole function. The graph of f(x) + k is the graph of f(x) moved up by k when k is positive, and down by |k| when k is negative. The shift acts on the output, which is why it is vertical — it changes the height of every point.

This is the simplest of the graph transformations and a good one to anchor the rest. Adding outside the function moves it vertically; the parallel move that comes from changing the input is horizontal instead, and it behaves in a surprisingly opposite way.