To transform a function vertically, you add a number to or subtract a number from the entire function, or multiply it by a number. To do something to an entire function, say


Now, you make all vertical transformations by placing a number somewhere on the right side of the equation outside the parentheses. (Obviously, you don’t actually need the parentheses.)

Unlike horizontal transformations, vertical transformations work the way you’d expect: adding makes the function go up, subtracting makes it go down, multiplying by a number greater than 1 stretches the function, and multiplying by a number less than 1 shrinks the function. For example:


Multiplying the function by –1 reflects it over the x-axis, or, in other words, flips it upside down. All points of the function jump over the x-axis and end up on the opposite side, the same distance from the axis. Original points that lie on the x-axis (the x-intercepts) do not move.