# What is an asymptote?

Oct 22, 2015

An asymptote is a limit on a function so that the function will never touch the line at the asymptote, but will get infinitely close.

#### Explanation:

I'll use this section for examples and extra explaining.
Take the function $y = \frac{x}{x + 4}$

We know that $x \ne - 4$ as if it were the function would be undefined. This is an asymptote in the graph.

Basically it is an invisible line that the graph cannot touch no matter what. However, the function can appear on the other side (as seen in the above equation).

An asymptote can be found by evaluating what makes the denominator = 0. In the above function it is -4. We also need to make sure that those values that make the denominator = 0 do not make the numerator = 0, as those would be holes in the graph, which are different.

Hope this helped!
The text provides a definition and explanation of what an asymptote is, including an example function and conditions for identifying asymptotes. It does not contain any mathematical questions or answers to such questions.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# What is an asymptote?

Oct 22, 2015

An asymptote is a limit on a function so that the function will never touch the line at the asymptote, but will get infinitely close.

#### Explanation:

I'll use this section for examples and extra explaining.
Take the function $y = \frac{x}{x + 4}$

We know that $x \ne - 4$ as if it were the function would be undefined. This is an asymptote in the graph.

Basically it is an invisible line that the graph cannot touch no matter what. However, the function can appear on the other side (as seen in the above equation).

An asymptote can be found by evaluating what makes the denominator = 0. In the above function it is -4. We also need to make sure that those values that make the denominator = 0 do not make the numerator = 0, as those would be holes in the graph, which are different.

Hope this helped!
user
The text provides a definition and explanation of what an asymptote is, including an example function and conditions for identifying asymptotes. It does not contain any mathematical questions or answers to such questions.

TYPE: NO_QUESTION