Graphing Rational Functions

I. Rational Functions Let P(x) and Q(x) be polynomial functions with no common factors and, then is a rational function.

II. Graphing Procedure Rational Functions A.) Follow steps A-E from yesterday. F.) Find r such that Q(x) = 0. x = r is a vertical asymptote. G.) If L exists, then y = L is a horizontal asymptote.

H.) Use A – G to plot an ACCURATE graph. Plot additional points if necessary.

III. Examples A.) Ex. – Use the graphing procedure to graph the following function. Step A.) Step B.)

C.) D.) y-int: x-int: E.) Sym:

F.) G.)

B.) Ex. – Use the graphing procedure to graph the following function. Step A.) Step B.)

C.) D.) y-int: x-int: E.) Sym:

F.) G.)