Originally Posted by
Reckoner Do you mean $\displaystyle y = \frac{1}{x} - 3$ (as it's written) or $\displaystyle y = \frac{1}{x - 3}$?
In either case, the domain is the set of values of $\displaystyle x$ for which the function is defined. Notice that you have a variable in the denominator of your function. Since division by zero is undefined, what does that tell you about the values that $\displaystyle x$ can take on?
The range will be all of the possible values of $\displaystyle y$. For $\displaystyle y = \frac{1}{x} - 3$, note that $\displaystyle \frac{1}{x}$ can never be zero; what does that tell you about the possible values of $\displaystyle y$?