# How do you find the end behavior of f(x)= (3x+1)/x?

Jan 11, 2016

${\lim}_{x \rightarrow - \infty} \frac{3 x + 1}{x} = 3$

${\lim}_{x \rightarrow + \infty} \frac{3 x + 1}{x} = 3$

$\therefore y = 3$ horizontal asymptote

#### Explanation:

To find the end behavior of $f \left(x\right)$ you have to evaluate:

${\lim}_{x \rightarrow \pm \infty} f \left(x\right)$

1. ${\lim}_{x \rightarrow - \infty} \frac{3 x + 1}{x} \approx {\lim}_{x \rightarrow - \infty} \frac{3 x}{x} = 3$

2. ${\lim}_{x \rightarrow + \infty} \frac{3 x + 1}{x} \approx {\lim}_{x \rightarrow + \infty} \frac{3 x}{x} = 3$

Therefore

$y = 3$ is an horizontal asymptote

graph{(3x-1)/x [-8.72, 7.08, -1.28, 6.62]}