Rational Functions Review

Flashcard
•
Mathematics
•
12th Grade
•
Hard
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a rational function?
Back
A rational function is a function that can be expressed as the quotient of two polynomials, i.e., \( f(x) = \frac{P(x)}{Q(x)} \) where \( P(x) \) and \( Q(x) \) are polynomials.
2.
FLASHCARD QUESTION
Front
What are the key characteristics of rational functions?
Back
Key characteristics include: points of discontinuity, vertical asymptotes, horizontal asymptotes, zeros, and the domain.
3.
FLASHCARD QUESTION
Front
How do you find the vertical asymptotes of a rational function?
Back
Vertical asymptotes occur where the denominator is zero and the numerator is not zero. Solve \( Q(x) = 0 \) to find these points.
4.
FLASHCARD QUESTION
Front
What is a horizontal asymptote?
Back
A horizontal asymptote describes the behavior of a function as \( x \) approaches infinity. It can be found by comparing the degrees of the numerator and denominator.
5.
FLASHCARD QUESTION
Front
How do you determine the domain of a rational function?
Back
The domain of a rational function is all real numbers except where the denominator is zero.
6.
FLASHCARD QUESTION
Front
What is a point of discontinuity?
Back
A point of discontinuity occurs where a function is not continuous, often where the denominator is zero.
7.
FLASHCARD QUESTION
Front
How do you find the zeros of a rational function?
Back
Zeros of a rational function are found by setting the numerator equal to zero and solving for \( x \).
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