# 1.8: Limits and Asymptotes

Difficulty Level: At Grade Created by: CK-12
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Practice Limits and Asymptotes

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### Vocabulary Language: English

TermDefinition
$\infty$ The symbol "$\infty$" means "infinity", and is an abstract concept describing a value greater than any countable number.
Asymptotes An asymptote is a line on the graph of a function representing a value toward which the function may approach, but does not reach (with certain exceptions).
Asymptotic A function is asymptotic to a given line if the given line is an asymptote of the function.
End behavior End behavior is a description of the trend of a function as input values become very large or very small, represented as the 'ends' of a graphed function.
Horizontal Asymptote A horizontal asymptote is a horizontal line that indicates where a function flattens out as the independent variable gets very large or very small. A function may touch or pass through a horizontal asymptote.
infinity Infinity is an unbounded quantity that is greater than any countable number. The symbol for infinity is $\infty$.
limit A limit is the value that the output of a function approaches as the input of the function approaches a given value.
Oblique Asymptote An oblique asymptote is a diagonal line marking a specific range of values toward which the graph of a function may approach, but generally never reach. An oblique asymptote exists when the numerator of the function is exactly one degree greater than the denominator. An oblique asymptote may be found through long division.
Oblique Asymptotes An oblique asymptote is a diagonal line marking a specific range of values toward which the graph of a function may approach, but generally never reach. An oblique asymptote exists when the numerator of the function is exactly one degree greater than the denominator. An oblique asymptote may be found through long division.
Piecewise Function A piecewise function is a function that pieces together two or more parts of other functions to create a new function.
Slant Asymptote A slant asymptote is a diagonal line marking a specific range of values toward which the graph of a function may approach, but will never reach. A slant asymptote exists when the numerator of the function is exactly one degree greater than the denominator. A slant asymptote may be found through long division.
Vertical Asymptote A vertical asymptote is a vertical line marking a specific value toward which the graph of a function may approach, but will never reach.

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