Rational Function Graphs

Flashcard
•
Mathematics
•
11th Grade
•
Hard
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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, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials and Q(x) ≠ 0.
Tags
CCSS.HSF-IF.C.7D
2.
FLASHCARD QUESTION
Front
What is the general form of a rational function?
Back
The general form of a rational function is f(x) = \frac{P(x)}{Q(x)}, where P(x) and Q(x) are polynomials.
Tags
CCSS.HSF-IF.C.7D
3.
FLASHCARD QUESTION
Front
What is an asymptote in the context of rational functions?
Back
An asymptote is a line that a graph approaches but never touches. For rational functions, there are vertical and horizontal asymptotes.
Tags
CCSS.HSF-IF.C.7D
4.
FLASHCARD QUESTION
Front
How do you find vertical asymptotes of a rational function?
Back
Vertical asymptotes occur where the denominator Q(x) = 0, provided that the numerator P(x) is not also zero at those points.
Tags
CCSS.HSF-IF.C.7D
5.
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.
Tags
CCSS.HSF-IF.C.7D
6.
FLASHCARD QUESTION
Front
How do you determine the horizontal asymptote of a rational function?
Back
To find the horizontal asymptote, compare the degrees of the numerator and denominator: If degree of P < degree of Q, y=0; if degree of P = degree of Q, y = leading coefficient of P / leading coefficient of Q; if degree of P > degree of Q, there is no horizontal asymptote.
Tags
CCSS.HSF-IF.C.7D
7.
FLASHCARD QUESTION
Front
What does the transformation f(x) = \frac{1}{x - 2} represent?
Back
This transformation represents a horizontal shift of the basic rational function f(x) = \frac{1}{x} to the right by 2 units.
Tags
CCSS.HSF.BF.B.3
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