5.2.Lesson_QuotientsofPolynomials.notebook
1
October 23, 2009
5.2 Exploring Quotients of Polynomial Functions
Definition:
A
rational function
is a function that can be expressed as
where
p(x)
and
q(x)
are polynomial functions,
q(x)
≠0.
When we divide two polynomial functions, the rational function that is
created could have one or more of the following discontinuities:
•
Vertical Asymptotes (vertical
lines
where the function is undefined)
•
Holes (
points
where the function is undefined)
•
Horizontal asymptotes
•
Oblique asymptotes
DISCONTINUOUS RATIONAL FUNCTIONS
(A)
Rational Functions with Holes
•
Holes will occur in a graph of a function when the indeterminate
form
occurs.
•
How do we know where there is a hole in a function?
Example #1:
Sketch the graph of the function
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October 23, 2009
Example #2:
Find the holes and vertical asymptote for the following
function. Use the information to sketch the function.
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 Spring '11
 sda
 Polynomials

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