Problem:
Compare the graphs of the functions

f(x) = (7x3 - 5x2 + 7x + 11)/(x5 - 11x + 2)
and
k(x) = 7/x2

by zooming out several times.

Visualization:
In the following LiveMath Notebook, you can view the graphs of y = f(x) (blue graph) and y = k(x) (red graph). You can zoom out by clicking on the rocket ship which is at the upper right-hand corner of the notebook. The graph will compress quickly in the horizontal direction. In this case, you may want to zoom in using the knife in the upper right-hand corner so that the graph fills up the notebook. You should be able to zoom out so that the two graphs appear to coincide.

You can change the function in the notebook above. Try

• changing in f, x3 to x6, and changing k to 7x;
• changing in f, x3 to x7, and changing k to 7x2;
• changing in f, x3 to x8, and changing k to 7x3;
[To change the definition of k(x) in the notebook above, highlight the right-hand side of the equation in the second equation and then type in the new function. For example, to enter k(x) = 7 x2, you will need to type in

7x^2.

After you enter an exponent, you will need to move the blinking cursor with the mouse from the exponent to the side.]