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What are the asymptotes of #y=(2x^2 +1)/( 3x -2x^2)#?

Answer 1

Julia Adams

Vertical Asymptotes:
#x= 0^^x=-3/2#

Horizontal Asymptote:

#y=-1#

#y=(2x^2+1)/(3x-2x^2)=-(2x^2+1)/(2x^2+3x)=-(2x^2+1)/(x(2x+3))#

#x(2x+3)=0#

Thus,

#x=0#

#(2x+3)=0=>x=-3/2#

asymptotes that are vertical.

We have a horizontal asymptotes since the degree of the numerator and denominator is the same.

#y~~-(2x^2)/(2x^2)=-1#

#:.y=-1# is a horizontal asymptotes for #xrarr+-oo#

graph{-x(2x+3))/(2x^2+1) [-25.66, 25.65, -12.83, 12.82]}

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Answer 2

Kennedy Adams

The rational function (y = \frac{2x^2 + 1}{3x - 2x^2}) has vertical asymptotes at (x = 0) and (x = \frac{3}{2}) and no horizontal asymptotes.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.