Problem:
Given the following function

graph the three functions y = f(x), y = f(-x), and y = -f(-x) and see if any two of the graphs coincide.


Visualization:
Using Derive,

  1. Prepare the program for graphics.
  2. If the first menu item is Algebra then press .
  3. Press for Author.
  4. Enter the function
    f(x) := sin(x) + 4x^3
  5. Press twice to get the graph. Note the color of the graph.
  6. Press twice and enter
    f(-x)
  7. Press twice to get the graph. Again note the color of the graph.
  8. Press twice and enter
    -f(-x)
  9. Press twice to get the graph. Again note the color of the graph.

It appears from the drawing of the latter graph that the two functions y = f(x) and y = -f(-x) are the same. Hence, it appears that the function y = f(x) is odd.