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# 2.7: Graphs of Rational Functions

Difficulty Level: At Grade Created by: CK-12
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Practice Graphs of Rational Functions

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Estimated8 minsto complete
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Estimated8 minsto complete
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### Vocabulary Language: English

TermDefinition
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).
compression A stretch or compression is a function transformation that makes a graph narrower or wider, without translating it horizontally or vertically.
domain The domain of a function is the set of $x$-values for which the function is defined.
Function A function is a relation where there is only one output for every input. In other words, for every value of $x$, there is only one value for $y$.
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.
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.
Polynomial Function A polynomial function is a function defined by an expression with at least one algebraic term.
Reflection Reflections are transformations that result in a "mirror image" of a parent function. They are caused by differing signs between parent and child functions.
shift A shift, also known as a translation or a slide, is a transformation applied to the graph of a function that does not change the shape or orientation of the graph, only the location of the graph.
shifts A shift, also known as a translation or a slide, is a transformation applied to the graph of a function that does not change the shape or orientation of the graph, only the location of the graph.
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.
stretch A stretch or compression is a function transformation that makes a graph narrower or wider.
Transformations Transformations are used to change the graph of a parent function into the graph of a more complex function.
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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