How do you find all the asymptotes for function #y=(3x^2+2x-1)/(x^2-4 )#?

1 Answer

Answer:

Vertical asymptotes are #x+2=0# and #x-2=0#. Horizontal asymptote is given by #y=3#

Explanation:

To find all the asymptotes for function #y=(3x^2+2x−1)/(x^2−4)#, let us first start with vertical asymptotes, which are given by putting denominator equal to zero or #x^2-4=0# i.e. #x+2=0# and #x-2=0#.

As the highest degree of both numerator and denominator is #2# and ratio of these is #3x^2/x^2# i.e. #3#, horizontal asymptote is given by #y=3#.

Vertical asymptotes are #x+2=0# and #x-2=0#. Horizontal asymptote is given by #y=3#

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I hope you do not mind but I added a graph.( Tony B)
Tony B