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RATIONAL FUNCTIONS!

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by

Puneet Gill

on 20 October 2013

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Transcript of RATIONAL FUNCTIONS!

RATIONAL FUNCTIONS!
Navnit, Puneet, Ishween, and Manroop!

Chapter 3.1 Reciprocal of a Linear Function
Chapter 3.2 : Reciprocals of Quadratics
A rational function - defined by rational fraction
Rational Functions of the Form :
(ax + b)/(cx + d)

KEY FEATURES :
Vertical Asymptote : -d/c
Horizontal Asymptote: a/c
Y – intercept : b/d
X – intercept: -b/a

Chapter 3.3
How To Graph Rational Functions :
Domain

Plot V.A. and H.A.

Calculate/Investigate Limits

Perform a 'End Behavior' Chart

Calculate Y-intercept

DRAW GRAPH !!!!

Range
3 possibilities of quadratic expressions;
x + 3x - 4
2
x + 21x + 1
2
factorable
perfect square factor
not factorable
(x - 1) (x + 4)
(x + 8)
x + 21x + 1
2
x² + 16x + 64
2
What's a Reciprocal of Quadratic Function?
function in the form of
f(x)=
g/ Quadratic

*g can represent any number

A Quadratic?
"Solve" the denominator by
factoring
An example...
perfect square factor
GRAPHING THE FUNCTION...
5 STEPS:
Find the
Domain
of the function
Include restrictions on x that makes f(x)=0
Solve for the
LIMITS

As x -> 5 from +/- side, f(x) -> -/+ infinity
Determine the
End Behaviours
Substitute x=1000,10000,100000 to analyze if f(x)-> 0 from +/- side of x-axis
Use the
"Zmoofab Method"
Legitimize
the graph!
State the
Range
of the function!
*TARGET*
Aim to finish the question in 10 minutes!
KEY FACTS!

Factorable Quadratic Rational Function ALWAYS has
"Line Symmetry"
Function may cross the Horizontal Asymptote
An Example:
Our original equation
Factor the equation
State restrictions
1. State the Domain!
2. Find Limits
This trend will be seen on the graph!
g(x)
Any Questions?

Thank You for listening! :)

a function of the form;
a
______
(mx - n)
2
only one factor, so only one asymptote.
in this case, the asymptote would lie at n
_
m
unfactorable expression
assess x towards the asymptote (1.5)
assess x towards the infinities
Domain = {x e R | x =/= 1.5 }
Range = {y e R | y > 0}
f(x) =
a function of the form
a
________
px + qx + r
f(x) =
Domain = {x e R} since the discriminant < 0
"the speed bump graph"
H.A. : y = 0
V.A. : x = 1.5
Range = {y e R | 0 > y >= 1/5}
Only assess x towards the infinities
Find your maximum value by making the denominator the smallest possible value (for this instance, it would be at x = 0), making your maximum value 1/5 (0.2).
H.A.: y = 0
Forms
f(x)= P(x)
Q(x)
Example
g(x)= 1
x+7
VA: x= -7
HA: y= 0

Reciprocal of a Linear Function
Restrictions: x= c
k
Vertical Asymptote: x= c
k
Horizontal Asymptote: y= 0
f(x)= 1
kx-c
As x g(x)
-7^+ +inf
-7^- -inf
+inf 0 from above
-inf 0 from below
2
hi
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