Problem:
Provide graphical explanations in interpreting the following expression as a function.

f(x) = x3 - x


Visualization:
Using The Function Visualizer:
  1. The program has the function g(x) = sin(x) as the default function. We change this by moving the mouse so that the cursor lies in the black rectangle at the bottom of the screen and then click the left button on the mouse.
  2. A prompt is placed on the end of the expression sin(x); use the backspace key to delete this expression.
  3. Enter

    x^3-x

  4. We will now change the domain. Move the mouse so that the cursor lies in the small rectangle which lies above the big square on the left on the left side. Click the left button on the mouse.
  5. A prompt is placed on the end of the expression; use the backspace key to delete this expression.
  6. Enter the maximum value of the domain:

    1.2

  7. We now repeat the above three steps to change the minimum value of the domain but we use the small rectangle which lies below the big square on the left on the left side. Enter: -

    -1.2

  8. Using the mouse, move the cursor into the big square on the left. As you move the mouse in this square, note the line which connects a number in the domain with its image in the range. Also note the graph on the right.

  9. Choosing the Point Trail option (by moving the cursor with the mouse to the latter item and clicking on the left button), then if we repeat the previous step and click on the left button of the mouse, then several dotted lines will be drawn so that we can check the value of the function at several values.

  10. By choosing the Animated Interval, then we can check the value of the function at all points of the domain.