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For each functon find the following (if they exist).

     a. End Behavior including the equations of horizontal or slant asymptotes.

     b. Vertical Asymptote(s). Distinguish between VA and Holes.

 

f(x)=3x3x34x

 Nov 15, 2017
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For each functon find the following (if they exist).

     a. End Behavior including the equations of horizontal or slant asymptotes.

     b. Vertical Asymptote(s). Distinguish between VA and Holes.

 

 

y=3x3x34xy=3x3x(x2)(x+2) sox±2,x0 y=3x3x34x

 

 

 

y=3x3÷x3(x34x)÷x3y=314x2limx0±y=31=0Hole at (0,0)limx±y=310=3 Let δ be a miniscule positive number.limx2+y=31(1δ)=3δ=limx2y=31(1δ)=3δ=limx2y=31(1+δ)=3δ=limx2+y=31(1+δ)=3δ=
 

Hole at (0,0)

Vertical asymptotes at  x=+2 and x=-2

Horizontal asymptotes at  y=-3

 

Here is the graph

 

 Nov 15, 2017

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