Ch. 9 Rational Functions
Lesson 1 Rational Functions Using Transformations
Rational Function:
A function that can be written in the form f ( x) =
q(x) are polynomial expressions and q( x) ¹ 0 .
Example(s):
Graph a Rational Function Using a Table of Values
Ex.
x
-12
-6
-3
-2
-1
-0.5
-0.1
0
0.1
0.5
1
2
3
6
12
y=
y
6
x
p ( x)
, where p(x) and
q ( x)
Characteristic
y=
6
x
Non-Permissible Value (NPV)
Behaviour near NPV
End Behaviour
Domain
Range
Equation of vertical asymptote
Equation of horizontal asymptote
Base Function:
Ex.
y=
1
x
Graph the function y =
®
y=
6
-3
x-2
a
+ k represents the transformation:
x-h
Graph a Rational Function With Linear Expression in Numerator AND Denominator
Ex.
Graph the function y =
4x - 5
. Identify any asymptotes and intercepts.
x-2