Vertical Asymptotes and Limits

Flashcard
•
Mathematics
•
12th Grade
•
Hard
Standards-aligned
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15 questions
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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 does not have a defined value at x = a.
Tags
CCSS.HSF-IF.C.7D
2.
FLASHCARD QUESTION
Front
What does it mean for a limit to be undefined?
Back
A limit is undefined when the function does not approach a specific finite value as the input approaches a certain point, often due to a vertical asymptote.
3.
FLASHCARD QUESTION
Front
What are left-hand and right-hand limits?
Back
Left-hand limit refers to the value that a function approaches as the input approaches a certain point from the left (x -> a-). Right-hand limit refers to the value that a function approaches as the input approaches from the right (x -> a+).
4.
FLASHCARD QUESTION
Front
How do you determine the existence of a vertical asymptote?
Back
To determine the existence of a vertical asymptote, find values of x that make the denominator of a rational function zero while ensuring the numerator is not zero at those points.
Tags
CCSS.HSF-IF.C.7D
5.
FLASHCARD QUESTION
Front
What is the significance of the directions of limits at a vertical asymptote?
Back
The directions of limits (left-hand and right-hand) at a vertical asymptote indicate the behavior of the function as it approaches the asymptote, helping to understand whether it goes to positive or negative infinity.
Tags
CCSS.HSF-IF.C.7D
6.
FLASHCARD QUESTION
Front
Provide an example of a function with a vertical asymptote.
Back
An example is f(x) = 1/(x-2), which has a vertical asymptote at x = 2.
Tags
CCSS.HSF-IF.C.7D
7.
FLASHCARD QUESTION
Front
What happens to the graph of a function at a vertical asymptote?
Back
At a vertical asymptote, the graph of the function will approach infinity or negative infinity, creating a break in the graph.
Tags
CCSS.HSF-IF.C.7D
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