What are the asymptotes of $y = \frac{x^{2}}{x^{2} - 1}$ $y=x^2/(x^2-1)$ and how do you graph the function?

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What are the asymptotes of $y = \frac{x^{2}}{x^{2} - 1}$ $y=x^2/(x^2-1)$ and how do you graph the function?

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Answer 1 · 2017-04-28T10:43:33

$x^{2} - 1$ $x^2-1$ can be factorized into $(x - 1) (x + 1)$ $(x-1)(x+1)$

Explanation:

Both $x = + 1$ $x=+1$ and $x = - 1$ $x=-1$ are the vertical asymptotes, as they would make the denominator $= 0$ $=0$ and the function undefined.

As $x$ $x$ gets larger (positive or negative) the function looks more and more like $\frac{x^{2}}{x^{2}} = 1$ $x^2/x^2=1$ , so $y = 1$ $y=1$ is another (horizontal) asymptote.

graph{x^2/(x^2-1) [-10, 10, -5, 5]}

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What are the asymptotes of $y = \frac{x^{2}}{x^{2} - 1}$ $y=x^2/(x^2-1)$ and how do you graph the function?

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What are the asymptotes of $y = \frac{x^{2}}{x^{2} - 1}$ $y=x^2/(x^2-1)$ and how do you graph the function?