1. Horizontal Asymptotes
Algebra 2/Trigonometry
Section 9.2, 9.3 Rational Functions – Notes Day 2
The degree of the each polynomial, N(x) and D(x), allows us to determine if we have an Horizontal Asymptote (H.A.) OR a Slant Asymptote (S.A.).
Horizontal Asymptotes
The graph of a rational function will have horizontal asymptotes whenever the leading power on the bottom is _____________ _____________ or ______________ to the leading power on the top.
CASE 1: Denominator Degree is Greater If the bottom degree is greater than the top degree, then the horizontal asymptote is
_____________ (the __________).
Examples:
Vertical Asymptotes
Horizontal Asymptotes 1. 2.
CASE 2: Degrees are Equal
If the bottom degree is _____________ the top degree , the horizontal asymptote is
y = ____________________________________________.
Examples
Vertical Asymptotes
Horizontal Asymptotes 1. 2.

2. Ex. 1: Ex. 2: S.A. _____________ S.A. _____________ V.A. _____________
Slant Asymptotes
Numerator Degree is Greater
If the leading top degree is ____________________________ more than the leading bottom degree, then the graph will have a slant asymptote.
Procedure to find the slant asymptote:
1) ___________________________ 2) ____________________ 3) _____________________
Ex. 1: Ex. 2:
S.A. _____________
S.A. _____________
V.A. _____________
V.A. _____________
Ex. 3
S.A. ___________________ V.A. ____________________ Hole(s): _____________
Ex. 4: Ex. 5:
S.A. ______________________________ S.A. ______________________________