
Asymptotes of Rational Functions
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a horizontal asymptote?
Back
A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity.
2.
FLASHCARD QUESTION
Front
How do you find the horizontal asymptote of a rational function?
Back
To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the denominator, the asymptote is y=0. If they are equal, the asymptote is y=\frac{a}{b}, where a and b are the leading coefficients.
3.
FLASHCARD QUESTION
Front
What is a vertical asymptote?
Back
A vertical asymptote is a vertical line that the graph of a function approaches as the input (x) approaches a certain value, typically where the function is undefined.
4.
FLASHCARD QUESTION
Front
How do you find vertical asymptotes in a rational function?
Back
Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving for x.
5.
FLASHCARD QUESTION
Front
What does it mean if a function has a non-removable discontinuity?
Back
A non-removable discontinuity occurs at a vertical asymptote where the function approaches infinity or negative infinity, and cannot be 'fixed' by redefining the function at that point.
6.
FLASHCARD QUESTION
Front
What is the end behavior of a function?
Back
The end behavior of a function describes how the function behaves as x approaches positive or negative infinity.
7.
FLASHCARD QUESTION
Front
What is the significance of the leading coefficient in determining horizontal asymptotes?
Back
The leading coefficient of the numerator and denominator helps determine the horizontal asymptote when the degrees of both are equal.
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