# How do you find the asymptotes for h(x) = (2x+3)/(3x+1 )?

Apr 13, 2016

$\textcolor{b l u e}{\text{Vertical asymptote at } x = - \frac{1}{3}}$

$\textcolor{b l u e}{\text{Horizontal asymptote at } y = \frac{2}{3} \to 0.66 \overline{6}}$

#### Explanation:

The equation becomes undefined at $x = - \frac{1}{3}$
The denominator is not 'allowed' to become 0

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As absolute $x$ becomes increasingly larger the +3 and +1 become insignificant.

So ${\lim}_{x \to \pm \infty} \frac{2 x + 3}{3 x + 1} \to \frac{2}{3} \times \frac{x}{x} = \frac{2}{3}$

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$\textcolor{b l u e}{\text{Vertical asymptote at } x = - \frac{1}{3}}$

$\textcolor{b l u e}{\text{Horizontal asymptote at } y = \frac{2}{3} \to 0.66 \overline{6}}$