The Effects of Some Simple Compositions on the Graph of a Function

How are the graphs of , , , , , , , and related to the graph of ? These important ideas from a precalculus course are illustrated using various common functions including , , and . The graphs of these functions can be translated vertically and horizontally to provide many more examples of . The reset button puts a previously translated graph back to its original position.

Contributed by: Marc Brodie (Wheeling Jesuit University)