Problem:
Determine for what value(s) of a is the function

continuous.


Visualization:
Use the following LiveMath Notebook to change the value of a. Recall that the method that most programs use to draw the graphs of functions is by connecting pairs of consecutive points with straight lines. In the graph below, we see a vertical line at x = 3; this vertical line is not a part of the graph but results from this method of drawing graphs. Thus, the limit of the function f as x approaches 3 does not exit. (Why?) Therefore, to make the function f continuous, we need to choose a so that the two pieces of the graph are connected or joined together. In other words, there must be no vertical line segment at x = 3. View an animation to see how this can be done.