Math 103 College Algebra Worksheet 4.5. Rational Functions

Math 103 College Algebra Worksheet
4.5. Rational Functions
Name:
Definition:
A rational function is a function of the form _____________ where _____________________________________. The graph of
a rational function is continuous within each interval where the function is defined.
The Domain
The domain of the rational function
is _________________________________________.
Why?
Asymptotes: An asymptote of a graph of f(x) is a line that the graph of f(x) gets “closer and closer to” as points on the graph get
“farther and farther away” from the origin. There are THREE types of asymptotes with rational functions:
1. Vertical asymptotes: x = k, where k is a zero of the denominator (and not of the numerator).
Why?
Example:
2. Horizontal asymptotes:
a. y = 0 (the x-axis) if _________________________________.
Why?
b. ____________________________________ if the degrees of the numerator and the denominator are equal.
Why?
c.
If the degree of the numerator is larger than the degree of the denominator, ______________________.
Why?
3. Oblique asymptotes (slant asymptotes):
An oblique asymptote exists ONLY when ________________________________, and it is the quotient when
____________ is divided by ____________.
Why?
Let’s practice.
1. = 2. = 3. = 4. =