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# Find the domain of the function and identify any vertical and horizontal asymptotes.$f(x)=\frac{3x^2+x-5}{x^2+1}$

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Given:

$f(x)=\frac{3x^2+x-5}{x^2+1}$

We need to determine the domain, vertical asymptotes, and horizontal asymptotes of the given function.

The domain consists of all $x$-values for which the function is defined.

$x=a$ is a vertical asymptote when the function approaches $-\infty$ or $+\infty$ as $x$ approaches $a$.

$y=b$ is a horizontal asymptote when the function approaches $b$ as $x$ approaches $-\infty$ or $+\infty$.

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