Problem:
Provide graphical explanations in interpreting the following expression as a
function.
f(x) = x^{3} - x
Visualization:
Using The Function Visualizer:
- 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.
- A prompt is placed on the end of the expression sin(x); use the
backspace key to delete this expression.
- Enter
x^3-x
- 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.
- A prompt is placed on the end of the expression; use the
backspace key to delete this expression.
- Enter the maximum value of the domain:
1.2
- 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
- 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.
- 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.
- By choosing the Animated Interval, then we can check the value of
the function at all points of the domain.