*Problem:*

Explore the graphs of the functions
**f(x) = x**^{3} - 5 x + a
for values of **a** between **-2** and **2** and determine for which
**a** the function is odd.

*Visualization:*

In the following LiveMath Notebook, you can view the graphs of **y = f(x)**
(blue graph) and **y = -f(-x)** (red graph). You can view the animation
which corresponds to changes in the values of **a** by moving the cursor
to the graph and clicking the left mouse button. When the two graphs coincide,
the function is odd. Note that the values of **a** appear in the upper
right corner of the notebook.
[If the animation is moving too fast for you to see the values of
**a**, click on item 6 frames/second at the bottom of
the notebook and slow down the animation.]

You can change the function in the notebook above. Try

- x
^{3}- 9x + a
- x
^{5}- 9x + a
- x
^{3}- 9x^{2} + a
- x
^{5}- 9x^{3} + a

[To change a coefficent in the definition of **f(x)** in the notebook above, highlight
the coefficent with the mouse and then type in the new coefficient. To change **x** to **x**^{2}, highlight **x** in the notebook with the mouse and press the shift and 6 keys at the same time followed by 2.]