Rational Functions and Asymptotes

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•
Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a rational function?
Back
2.
FLASHCARD QUESTION
Front
What is an asymptote?
Back
An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.
3.
FLASHCARD QUESTION
Front
How do you find vertical asymptotes of a rational function?
Back
Vertical asymptotes occur where the denominator of the rational function is zero and the numerator is not zero at those points.
4.
FLASHCARD QUESTION
Front
What is a horizontal asymptote?
Back
A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity.
5.
FLASHCARD QUESTION
Front
How do you determine the horizontal asymptote of a rational function?
Back
1. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. 2. If the degrees are equal, the horizontal asymptote is y = \frac{a}{b} where a and b are the leading coefficients. 3. If the degree of the numerator is greater, there is no horizontal asymptote.
6.
FLASHCARD QUESTION
Front
What is the domain of a rational function?
Back
The domain of a rational function is all real numbers except where the denominator is zero.
7.
FLASHCARD QUESTION
Front
How do you find the x-intercepts of a rational function?
Back
The x-intercepts occur where the numerator is zero (i.e., set P(x) = 0) and the denominator is not zero.
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