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

Feb 25, 2016

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 $3 {x}^{2} / {x}^{2}$ 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)