# What is the domain and range of f(x) = (x-1)/ (x^2 -x-6)?

Jun 6, 2017

${D}_{f} = \left[- \infty , + \infty\right] , x \notin \left[- 2\right] , \left[3\right]$

${R}_{f} = \left[- \infty , + \infty\right]$

#### Explanation:

Since we have a rational function, we know that we can't take values of $x$ for which the denominator equals $0$. We also know that there will be asymptotes as these $x$-values, so the range of the function will be over the reals

${x}^{2} - x - 6 = \left(x + 2\right) \left(x - 3\right)$

Thus $f$ will have asymptotes at $x = 3$ and $x = - 2$, so these aren't included in the domain. However, all other $x$-values are valid.