Problem:
Explore the graphs of the functions

f(x) = x3 - 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

• x3- 9x + a
• x5- 9x + a
• x3- 9x2 + a
• x5- 9x3 + 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 x2, highlight x in the notebook with the mouse and press the shift and 6 keys at the same time followed by 2.]