# What is the domain and range of  f(x) = ln (10-x)?

Domain $\left(- \infty , 10\right)$ Range $\left(- \infty , \infty\right)$
Since Ln of a negative number has no meaning, the maximum value that x can have is any number less than 10. At $x = 10$, the function becomes undefined. and the minimum value can be any negative number up to $- \infty$. At $x = 10$ there would be a vertical asymptote.
Hence domain would be $\left(- \infty , 10\right)$
The range would be $\left(- \infty , \infty\right)$