Graphing Rational Functions 

Factor the numerator and denominator (into linear factors if possible). Simplify. 
Use the factored form of the function (including any factors you have
canceled from the denominator) to determine the

Determine where the function is positive and where it is negative. 
Determine the behaviour of the function near the vertical asymptotes. 
Find the horizontal asymptote if there is one, and the behaviour of the function as x and as x. 
If f is defined at 0, find the yintercept,

With all the information you have accumulated about your function, you should now be ready to sketch the graph. The next exercise will lead you through the above steps.
At each stage, answer the questions in the box, then press NEXT. If you are asked for an intercept, asymptote or hole when there is none, press NEXT immediately. When you have completed all the questions, the software will tell you which are correct and which need to be fixed.
If something needs to be fixed, return to the appropriate page (by clicking the appropriate button), undo your previous answers by pressing UNDO to cancel the entry on that screen, and reenter the information.
Once all your information is correct, sketch the graph on paper. Then click on "Next" to see the graph on the computer and compare it with your sketch.
Graphing Rational Functions 

Note:
The rules that we have described here are helpful for all rational
functions for which the degree of the denominator is not smaller than
the degree of the numerator. However, these rules are not completely sufficient
for functions such as
In cases such as these, there may be other kinds of asymptotes: oblique straight lines, or even parabolas or higher degree polynomials! These are beyond the scope of the existing course, therefore we have not gone into detail regarding such graphs.