1. **Problem:** Find the range of the function $f(x) = |x|$. 2. **Formula and rules:** The absolute value function $|x|$ outputs the distance of $x$ from zero on the number line, which is always non-negative. 3. **Intermediate work:** For any real number $x$, $|x| \geq 0$. 4. **Explanation:** Since $|x|$ can be zero (when $x=0$) and can grow without bound as $x$ moves away from zero in either direction, the range is all real numbers greater than or equal to zero. 5. **Final answer:** The range of $f(x) = |x|$ is $[0, \infty)$.