SECTION 6.2GRAPHING RATIONALFUNCTIONS
HOW TO GRAPH RATIONAL FUNCTIONS:
Look at the Denominator and Find the VerticalAsymptote (VA) or NPV
◦Make the Denominator equal to zero and solve for “x”(Denominator can never be zero)
Use Long Division to Find the Horizontal Asymptotes(HA)
◦IF a Remainder exist, the Quotient is the HA
◦IF there is no Remainder, then no HA,the Quotient becomes the graph
Use patterns of Rational Functions to make a sketch ofthe graph OR
Make a Table of Values and plot points
EX: GRAPH THE FOLLOWING FUNCTION
1. Find the VA (Denominator)
2. Find the HA (Long Division)
x
y
-8
-4
0
4
8
12
16
-40
-20
20
40
60
x
y
-8
-4
0
4
8
12
16
-40
-20
20
40
60
Make a Table of Values with Points near the VA
PRACTICE: GRAPH THE FOLLOWING FUNCTION
1. Find the VA (Denominator)
2. Find the HA (Long Division)
EXAMPLE: GRAPH THE FOLLOWING FUNCTION
1. Find the VA (Denominator)
2. Find the HA (Long Division)
PRACTICE: GRAPH THE FOLLOWING FUNCTION
1. Find the VA (Denominator)
2. Find the HA (Long Division)
PRACTICE: GRAPH THE FOLLOWING FUNCTION
1. Find the VA (Denominator)
2. Find the HA (Long Division)
The function can besimplified and reduced!
The equation can besimplified to a straightline
At the asymptote, you get a“HOLLOW DOT” becauseyou can’t have a value for “x”at that point!
PRACTICE: GRAPH THE FOLLOWING FUNCTION
1. Find the VA (Denominator)
2. Find the HA (Long Division)
x
y
-8
-6
-4
-2
0
2
4
6
8
-2
-1
1
2
x
y
-8
-6
-4
-2
0
2
4
6
8
-2
-1
1
2
SUMMARY:
Find all the asymptotes first
Denominator Vertical &
Long Division Horizontal
Use the asymptotes to predict how the graph will lookOR
Plot some points to get a general idea of how the graphwill look
Note: If the degree of the numerator is larger, there isusually a slanted asymptote, unless the expressionsimplifies
If the degrees of the numerator and denominator arethe same, then there will be a horizontal asymptoteequal to the quotient of their coeffieicients