Asymptotes of Rational Functions

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•
Mathematics
•
11th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a vertical asymptote?
Back
A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates that the function is undefined at that point.
2.
FLASHCARD QUESTION
Front
How do you find vertical asymptotes of a rational function?
Back
To find vertical asymptotes of a rational function, set the denominator equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes.
3.
FLASHCARD QUESTION
Front
What is a horizontal asymptote?
Back
A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values of x.
4.
FLASHCARD QUESTION
Front
How do you find horizontal asymptotes of a rational function?
Back
To find horizontal asymptotes of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, y = 0 is the horizontal asymptote. If they are equal, divide the leading coefficients.
5.
FLASHCARD QUESTION
Front
What is the significance of asymptotes in graphing rational functions?
Back
Asymptotes help identify the behavior of the graph near undefined points and at extreme values, guiding the overall shape and direction of the graph.
6.
FLASHCARD QUESTION
Front
What is the difference between vertical and horizontal asymptotes?
Back
Vertical asymptotes indicate where a function is undefined and approaches infinity, while horizontal asymptotes indicate the value the function approaches as x goes to infinity.
7.
FLASHCARD QUESTION
Front
What is a rational function?
Back
A rational function is a function that can be expressed as the ratio of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials.
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