In your geometry course, you learned about “translations,” or what are sometimes referred to as “slides,” the movements of geometric shapes in the coordinate plane, by which all parts of a shape move in the same direction, and the same distance.

We do the same with the graphs of functions. For example, during your study of the graphs of quadratics, you examined the movement of the parabolic curves of quadratic functions, both horizontally and vertically, resulting in a new, or “translated” vertex. In algebraic terms, we identified such translations of one function to another as: , where the entire original function slides h units horizontally and k units vertically to a new location.

In the next topic, we will explore the translation and other transformation of the graphs of the basic trigonometric functions we just learned. As you will see, the processes are very similar you learned for other algebraic functions in this course.