Online Test Banks
Score higher
See Online Test Banks
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

How to Vertically Transform a Function

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.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus

Inside Sweepstakes

Win $500. Easy.