Shift - A rigid translation, the shift does not change the size or shape of the graph of the function. Translations of the common functionsĮach of the seven graphed functions can be translated by shifting, scaling, or reflecting: Make sure you are familiar with the shape and direction of each graph. Instead you will learn to recognize a given graph as, for example, the reflection of a graph of a cubic function. You will be able to do better mathematics faster, since you will save time not having to plot out individual points. Rather than get lost in the details, you will come to know the graphs of all seven functions, and their translations, as a group. The mathematics will not seem so intimidating. Rather than burden your brain by trying to memorize the configurations of some 28 different graphs (each original and three translations), concentrate on the changes each translation provides to its original function. In order to translate any of the common graphed functions, you need to recall and be fluent with the seven common functions themselves, presented here alphabetically because they are all equally important:Ībsolute Value Function: y = ∣ x ∣ y=\left|x\right| y = ∣ x ∣Ĭubic Function: y = x 3 y= y = x īy concentrating on the original seven functions and the way they appear when graphed, you will soon develop an awareness of how each of the three translations affects the original graphed function. Knowing how to shift, scale or reflect these graphs makes you a stronger mathematics student and produces many variations on the original graphs of common functions. Shifting, scaling and reflecting are three methods of producing translations for basic graphing functions you have already learned. Reflection - A mirror image of the graph of a function is generated across either the x-axis or y-axis Scale - The size and shape of the graph of a function is changed Shift - The graph of a function retains its size and shape but moves (slides) to a new location on the coordinate grid Translations are performed in three ways: Then, using translations, you can move the point.
Using the abscissa and ordinate, you can fix a point on the coordinate graph. This is the distance above or below the x-axis. Its partner is the ordinate, or y-coordinate. The abscissa is the x-coordinate, or the distance left or right from the y-axis that allows you to locate a point using a coordinate pair.