Pre-AP Pre-CalculusChapter 2, Section 6Graphs of Rational Functions2013 - 2014

Definition: Rational FunctionsLet f and g be polynomial

functions with . Then the function given by

is a rational function.

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.

The Reciprocal FunctionDomain:Range:Continuity:Decreasing:Symmetry:Local Extrema:Horizontal

Asymptote:Vertical Asymptote:End Behavior

𝑓 (𝑥 )=1𝑥

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.

𝑓 (𝑥 )= 2𝑥+3

𝑓 (𝑥 )=3 𝑥−7𝑥−2

Horizontal AsymptotesThe line is a horizontal

asymptote of a graph if the limit of the function as x approaches infinity is b.

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.

Finding AsymptotesFind the horizontal and vertical

asymptotes of

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

Domain:Range:Continuity:Decreasing:Symmetry:Local

Extrema:Horizontal

Asymptotes:Vertical

Asymptotes:End

Behavior:

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

Domain:Range:Continuity:Decreasing:Symmetry:Local

Extrema:Horizontal

Asymptotes:Vertical

Asymptotes:End

Behavior:

Long Division Practice

𝑓 (𝑥 )=𝑥3−3 𝑥2+3 𝑥+1𝑥−1

Ch. 2.6 HomeworkPg. 245 – 247: #’s 1, 11, 17, 21,

27, 37, 63, 65

8 Total Problems

Gray Book: