This preview shows pages 1–2. Sign up to view the full content.
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:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '09
 Johnson
 Algebra, Inverse Variation, Rational Functions

Click to edit the document details