Explore the graphs of the piecewise defined functions

for values of **a** between **-3** and **3**.

Note that the graph of **f** is, in general, in two pieces: a part of a
parabola and a part of a line. At **x = a**, LiveMath draws an additional
line segment from the end of parabola to the beginning of the other line; this
additional line is not a part of the graph. The correct graph would have a
break instead of the addtional line. In a later section, we'll see why
this line is drawn.

With this exploration you should become familiar with graphing a piecewise
defined function when you know the graphs of the two functions which are used
to define **f**.

- Substitute each of the values of
**-3, -2, -1, 0, 1, 3**for**a**in the definition of**f**above. View an animation to see how this can be done. - Which of these values for
**a**do the parabola and the line meet without using an additional line? - Explain why there are no other values for
**a**for which the parabola and the line meet without using an additional line; in other words, why there are no other values for**a**which gives you a graph which has no breaks in it.