# How do you find the domain, x intercept and vertical asymptotes of f(x)=ln(3-x)?

Mar 6, 2017

The domain is x in ]-oo,3[
The x intercept is $= \left(2 , 0\right)$
The vertical asymptote is $x = 3$

#### Explanation:

What's under the $\ln$ is $> 0$.

So,

$3 - x > 0$

$x < 3$

The domain of $f \left(x\right)$ is x in ]-oo,3[

When $f \left(x\right) = 0$

$\ln \left(3 - x\right) = 0$

$\ln 1 = 0$

$3 - x = 1$

$x = 3 - 1 = 2$

The x intercept is $= \left(2 , 0\right)$

As $x \ne 3$

The vertical asymptote is $x = 3$

graph{(y-ln(3-x))(y-1000(x-3))=0 [-3.033, 4.76, -1.84, 2.056]}