*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.