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Pre-AP Pre-CalculusChapter 2, Section 6Graphs of Rational Functions2013 - 2014
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Definition: Rational FunctionsLet f and g be polynomial
functions with . Then the function given by
is a rational function.
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Finding the domain of a rational functionFind the domain of f and use
limits to describe its behavior at value(s) of x not in its domain.
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The Reciprocal FunctionDomain:Range:Continuity:Decreasing:Symmetry:Local Extrema:Horizontal
Asymptote:Vertical Asymptote:End Behavior
𝑓 (𝑥 )=1𝑥
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Transforming the reciprocal functionOn the next couple of slides,
describe how the graph given has been transformed from . Identify any asymptotes and use limits to describe the corresponding behavior.
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𝑓 (𝑥 )= 2𝑥+3
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𝑓 (𝑥 )=3 𝑥−7𝑥−2
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Horizontal AsymptotesThe line is a horizontal
asymptote of a graph if the limit of the function as x approaches infinity is b.
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Horizontal Asymptote “tricks”If the higher degree is
on top, there is no horizontal asymptote.
If the higher degree is on the bottom, the horizontal asymptote is .
If the degrees are the same, the horizontal asymptote is the ratio of the coefficients of the highest degree.
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Finding AsymptotesFind the horizontal and vertical
asymptotes of
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Analyze the graph of a rational functionFind the intercepts, asymptotes, use limits to
describe the behavior, and analyze and draw the graph of the rational function
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Domain:Range:Continuity:Decreasing:Symmetry:Local
Extrema:Horizontal
Asymptotes:Vertical
Asymptotes:End
Behavior:
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Analyze the graph of a rational functionFind the intercepts, asymptotes, use limits to
describe the behavior, and analyze and draw the graph of the rational function
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Domain:Range:Continuity:Decreasing:Symmetry:Local
Extrema:Horizontal
Asymptotes:Vertical
Asymptotes:End
Behavior:
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Long Division Practice
𝑓 (𝑥 )=𝑥3−3 𝑥2+3 𝑥+1𝑥−1
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Ch. 2.6 HomeworkPg. 245 – 247: #’s 1, 11, 17, 21,
27, 37, 63, 65
8 Total Problems
Gray Book: