Vertical Asymptotes and Limits

Vertical Asymptotes and Limits

Assessment

Flashcard

Mathematics

12th Grade

Hard

CCSS
HSF-IF.C.7D

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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