Steps To Graph Rational Functions
1.
Make sure the numerator and denominator of the function are arranged in the correct
descending order of power.
2.
Find the Domain
a.
Factor the denominator of the function completely.
b.
Find the real zeros of the denominator by setting the factors equal to zero and solving.
c.
Write “Domain = {
x

x
≠
_______
}”
3.
Factor the numerator and denominator completely. Cancel any common factors between the
numerator and denominator. (After you have canceled factors, you are left with the reduced
function. Use the reduced
function for all remaining steps.) If there are no common factors,
then skip Step 4.
4.
Find any Holes
a.
Set any common factor found in Step 3 equal to zero and solve.
This is the
x
coordinate
for the hole.
b.
Substitute this
x
value back into the reduced
function found in Step 3.
This is the
y
coordinate
for the hole.
c.
Plot the hole on the graph as an open circle.
5.
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 Spring '08
 MatRoy
 Rational Functions, Elementary arithmetic, Limit of a function, horizontal asymptote

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