1. Properties of Rational Functions
Dr. Fowler  AFM  Unit 3-2
Properties of Rational Functions

2. Finding the Domain of any Function:
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Finding the Domain of any Function:

3. 3.6: Rational Functions and Their Graphs
Rational functions are quotients of polynomial functions. This means that rational functions can be expressed as
where p(x) and q(x) are polynomial functions and q(x)  0. The domain of a rational function is the set of all real numbers except the x-values that make the denominator zero. For example, the domain of the rational function
is the set of all real numbers except 0, 2, and -5.
This is p(x).
This is q(x).

4. EXAMPLE: Finding the Domain of a Rational Function
3.6: Rational Functions and Their Graphs
EXAMPLE: Finding the Domain of a Rational Function
Find the domain of each rational function. a.
Solution Rational functions contain division. Because division by 0 is undefined, we must exclude from the domain of each function values of x that cause the polynomial function in the denominator to be 0.
a. The denominator of is 0 if x = 3. Thus, x cannot equal 3. The domain of f consists of all real numbers except 3, written {x | x  3}.
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5. EXAMPLE: Finding the Domain of a Rational Function
3.6: Rational Functions and Their Graphs
EXAMPLE: Finding the Domain of a Rational Function
Find the domain of each rational function. a.
Solution Rational functions contain division. Because division by 0 is undefined, we must exclude from the domain of each function values of x that cause the polynomial function in the denominator to be 0.
b. The denominator of is 0 if x = -3 or x = 3. Thus, the domain of g consists of all real numbers except -3 and 3, written {x | x  - {x | x  -3, x  3}.
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6. EXAMPLE: Finding the Domain of a Rational Function
3.6: Rational Functions and Their Graphs
EXAMPLE: Finding the Domain of a Rational Function
Find the domain of each rational function. a.
Solution Rational functions contain division. Because division by 0 is undefined, we must exclude from the domain of each function values of x that cause the polynomial function in the denominator to be 0.
c. No real numbers cause the denominator of to equal zero. The domain of h consists of all real numbers.

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10. Oblique Asymptote
a.k.a. “Slant” Asymptote
Horizontal Asymptote
Vertical Asymptote
A vertical asymptote is a vertical line that doesn't intersect the graph of the function. 

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21. Excellent Job !!! Well Done