
Pre-Calc P1 HW:12.05.24: Graphs of Rational Functions

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Mathematics
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11th Grade
•
Hard
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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 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. It indicates the behavior of the function at extreme values of \( x \).
3.
FLASHCARD QUESTION
Front
How do you find horizontal asymptotes for rational functions?
Back
To find horizontal asymptotes of a rational function \( f(x) = \frac{P(x)}{Q(x)} \), compare the degrees of the polynomials \( P \) and \( Q \): 1. If degree of \( P < \) degree of \( Q \), then \( y = 0 \) is the horizontal asymptote. 2. If degree of \( P = \) degree of \( Q \), then \( y = \frac{a}{b} \) where \( a \) and \( b \) are the leading coefficients of \( P \) and \( Q \). 3. If degree of \( P > \) degree of \( Q \), there is no horizontal asymptote.
4.
FLASHCARD QUESTION
Front
What is a vertical asymptote?
Back
A vertical asymptote is a vertical line \( x = a \) where the function approaches infinity or negative infinity as \( x \) approaches \( a \). It occurs where the denominator of a rational function is zero.
5.
FLASHCARD QUESTION
Front
How do you find vertical asymptotes for rational functions?
Back
To find vertical asymptotes of a rational function \( f(x) = \frac{P(x)}{Q(x)} \), set the denominator \( Q(x) = 0 \) and solve for \( x \).
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. For example, for \( f(x) = \frac{1}{x-3} \), the domain is \( x \neq 3 \).
7.
FLASHCARD QUESTION
Front
How do you find the x-intercepts of a rational function?
Back
To find the x-intercepts of a rational function \( f(x) = \frac{P(x)}{Q(x)} \), set the numerator \( P(x) = 0 \) and solve for \( x \).
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