Question

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

Answer 1

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)