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Graphing Rational Functions
A rational function is defined here as a function that is equal to a ratio of two polynomials
p(x)/q(x) such that the degree of q(x) is at least 1.
Examples:
is a rational function since it is a ratio of two polynomials with degree in
the denominator greater than or equal to 1.
is
not
a rational function since the degree of the denominator is not
greater than or equal to 1.
is
not
a rational function since the numerator is not a polynomial.
Reduced Rational Functions
A reduced rational function is one where there are no factors common to the numerator
and denominator.
For example, y = (x –1)/(x
2
– 4)
is in reduced form since there is no
factor of (x1) in the denominator.
Example of NonReduced Form:
y = (x
2
– 4)/(x – 2) is in nonreduced form since it
may be written as
y =[(x + 2)(x2)]/(x2)
which may be reduced to
y = x + 2 after canceling common factors of (x2).
So the equation simplifies to a linear
equation! However, since x=2 results in division by zero in the original function, we are
missing the point at x=2.
The graphs of both y=x+2 and our rational function are shown
below.
TIP: Always simplify a rational function first, if possible.
And remember to
exclude any values of x from the domain that result in division by zero.
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The Simplest Rational Function: y = 1/x
If you graph the simplest rational function y = 1/x, you get the solution points and graph
shown (in blue) below:
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This note was uploaded on 11/30/2010 for the course CIIVIL WNG 33155 taught by Professor Y.bahie during the Spring '10 term at The British University in Egypt.
 Spring '10
 y.bahie

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