Problem:
Given the functions

draw the graphs of the functions f, g, fg, and gf.


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) := 1/(1+x^2)
  5. Press twice to get the graph.
  6. Press twice and enter
    g(x) := sin(x)
  7. Again press twice to get the graph.
  8. Press twice and enter
    f(g(x))
  9. Press twice to get the graph.
  10. Press twice and enter
    g(f(x))
  11. Press twice to get the graph.