9.3 Notes
Warmup:
Factor:
OBJECTIVES:
c
Identify properties of rational functions
c
Graph rational functions
An inverse variation is an example of a rational function!
24
19
2
2
+

=
x
x
y
Rational Function
c
Rational means – “ratio” which means “fraction”!
Rational Function:
where P(x) and Q(x) are polynomial functions
and Q(x) is NOT zero.
A polynomial divided by a polynomial
Example:
)
(
)
(
)
(
x
Q
x
P
x
f
=
1
2
)
(
2
+

=
x
x
x
f
Examples of graphs
1
2
)
(
2
+

=
x
x
x
f
4
1
2

=
x
y
1
)
1
)(
2
(
)
(
+

+
=
x
x
x
x
f
POINT OF DISCONTINUITY:
Find the values of x that make the
denominator = ?
Finding Points of Discontinuity
1
2
1
2
+
+
=
x
x
y
1)
2)
1
1
2
+
+

=
x
x
y
Discontinuity:
c
Breaks:
asymptotes create “breaks” in a graph.

where the denominator is equal to zero.
Ex:
c
Holes:
the same zero occurs in numerator and
denominator.
This x cannot occur – it creates a “hole” in our
graph.
Ex:
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 Fall '09
 Johnson
 Algebra, Inverse Variation, Rational Functions

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