# How do you graph y=(9x+1)/(3x-2) using asymptotes, intercepts, end behavior?

Apr 12, 2018

Horizontal Asymptote :$y = 3$
Vertical Asymptote: $x = \frac{2}{3}$

#### Explanation:

You can Horizontal asymptote by making denominator of the rational function to zero
$3 x - 2 = 0$
$x = \frac{2}{3}$

You can find Vertical asymptote by finding the ratio of leading coefficient in the numerator to leading coefficient of the denominator
$y = \frac{9}{3} = 3$

Y-intercept can be found by making $x = 0$
$\left(0 , - \frac{1}{2}\right)$

X-intercept can be found by making numerator =0
$9 x + 1 = 0$
$x = - \frac{1}{9}$
$\left(- \frac{1}{9} , 0\right)$

graph{y=(9x+1)/(3x-2) [-8.36, 11.64, -3.12, 6.88]}