Graphing Rational functions

A rational function is a function of the form: f(x)=p(x)/Q(x)

1. Simplify the function. Factor the numerator and denominator, then eliminate common factors.

2. Holes: a hole is apoint (x,y) at which there is a discontinuity in the graph. A hole occurs when there is a common factor between the numerator and denominator.

   For each factor you eliminated in step 1, there is a hole! Locate each hole:

   -To find the x-coordinate, set the x factor=0 and solve

   -To find the y-coordinate, substitute the x-coordinate into the simplified function

3. X intercept(s): The points where the graph crosses the x-axis and where y=0.

   Set the numerator = 0 and solve

4. Vertical Asymptote(s): Vertical boundary lines which the graph will not cross, written in the form x=a. These occur because the denominator of a fraction cannot equal 0

   Set the denominator = 0 and solve

5. Horizontal Asymptotes: Horizontal guidelines, written in the form y = a

   Follow the rules below:

   -Degree of p < of q: y=0

   -Degree of p = of q: y=c (the ratio of the leading coefficients

   -Degree of p > of q: no horizontal asymptote

6. Y intercept: The point where the graph crosses the y-axis and where x=0.

   Substitute 0 for x in the simplified equation and solve for y.