# How do you find the domain of f(x) = ( 9x+8)/(-9-8x)?

May 13, 2015

Start by finding the 'forbidden' values of $x$

The denominator of a fraction may not be zero, so let's see when it is:
$- 9 - 8 x = 0 \to - 9 = 8 x \to x = - \frac{9}{8}$
Answer : $x \ne - \frac{9}{8}$
This forms a vertical asymptote:
graph{(9x+8)/(-9-8x) [-10, 10, -5, 5]}

Extra : as you can see, there is also a horizontal asymptote at

$y = - \frac{9}{8}$. This has to do with the range of this function