What You Should Know About Rational Functions (Lesson 2-5)
1. How to find the y-intercept (if it exists)
Let x = 0 and reduce the rational expression. This is a coordinate, so be able
to write it in coordinate form ( 0, y-int)
2. How to find x-intercepts (if they exist)
Let the numerator equal zero if possible. Hint: if you can’t factor, simply
graph the numerator and find where it crosses the x-axis. These are
coordinate locations so write them in the form (x1, 0), (x2, 0), …
3. How to find holes (if they exist)
Holes exist when there are identical factors in the numerator and
denominator. Set those factors equal to zero and solve for x.
4. How to find vertical asymptotes (if they exist)
Any factors of the denominator which DO NOT divide into the numerator
indicate where there are vertical asymptotes. Set these factors equal to zero
and solve for x. These are vertical lines, so it is appropriate to write them as
x = a, x = b, etc.
5. How to find horizontal asymptotes (if they exist)
Compare the degree of the numerator (N) to the degree of the denominator
(D).

N < D : the horizontal asymptote is y = 0

N = D : the horizontal asymptote is the division of the leading
coefficients.

N > D : there is no horizontal asymptote
6. How to find slant asymptotes (if they exist)

If N > D by exactly 1, then there is a slant asymptote. To find it use
long division and divide the numerator by the denominator. Please
note, IGNORE THE REMAINDER. Since the slant asymptote is a line,
your answer should be in the form of y = mx + b