How do you find all the asymptotes for function $y = \frac{3 x^{2} + 2 x - 1}{x^{2} - 4}$ $y=(3x^2+2x-1)/(x^2-4 )$ ?

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How do you find all the asymptotes for function $y = \frac{3 x^{2} + 2 x - 1}{x^{2} - 4}$ $y=(3x^2+2x-1)/(x^2-4 )$ ?

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Answer 1 · 2016-02-25T10:16:58

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

Explanation:

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

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

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

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

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How do you find all the asymptotes for function $y = \frac{3 x^{2} + 2 x - 1}{x^{2} - 4}$ $y=(3x^2+2x-1)/(x^2-4 )$ ?

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Explanation:

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How do you find all the asymptotes for function y=(3x^2+2x-1)/(x^2-4 )y=3x2+2x−1x2−4y=(3x^2+2x-1)/(x^2-4 )?

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Explanation:

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How do you find all the asymptotes for function $y = \frac{3 x^{2} + 2 x - 1}{x^{2} - 4}$ $y=(3x^2+2x-1)/(x^2-4 )$ ?