Work Step by Step
We want to determine all real $x$ values for which $f(x)=|3x-6|$ is defined. Starting inside the absolute values, we can always multiply any real number by 3 and then subtract 6 from the result, so $3x-6$ is defined for all real $x$. We can take the absolute value of any real number, so $|3x-6|$ is also defined for any real $x$. Thus, the domain of $f$ is all real numbers, written as $(-\infty,\infty)$ in interval notation.