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Graphs of Rational Functions

Graphs of functions with x in the denominator of a fraction

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Vocabulary

compression

compression

A stretch or compression is a function transformation that makes a graph narrower or wider, without translating it horizontally or vertically.
Function

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

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

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

Polynomial Function

A polynomial function is a function defined by an expression with at least one algebraic term.
Reflection

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

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

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

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

stretch

A stretch or compression is a function transformation that makes a graph narrower or wider.
Transformations

Transformations

Transformations are used to change the graph of a parent function into the graph of a more complex function.
Vertical Asymptote

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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