8-3 The Reciprocal Function Family

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General Form of a Rational Function

Points of discontinuity (POD) = values that make the denominator zero.

Holes: Removable PODVertical Asymptote(s): Non-removable POD

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xQ

xPy

Ex) Identify the points of discontinuity,holes and vertical asymptotes. Find the x-intercept and y-intercept.

34

32

xx

xy

Horizontal Asymptote: if…• degree of numerator <degree of denominator : y=0• degree of numerator >degree of denominator : none• degree of numerator =degree of denominator : y=a/b, where a=leading coefficient of numerator, b is leading coefficient of denominator.

Ex) Identify the points of discontinuity, holes,vertical asymptotes, horizontal asymptotes,x-intercept, y-intercept. Then graph.

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2

Ex) Identify the points of discontinuity, holes,vertical asymptotes, horizontal asymptotes,x-intercept, y-intercept. Then graph.

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x

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