1. **Problem:** Find the range of the function $$f(x) = \left| x - \frac{1}{2} \right| - 2$$. 2. **Formula and rules:** The absolute value function $$|x|$$ is always non-negative, so $$|x - \frac{1}{2}| \geq 0$$ for all $$x$$. 3. **Intermediate work:** Since $$|x - \frac{1}{2}| \geq 0$$, the smallest value of $$f(x)$$ occurs when $$|x - \frac{1}{2}| = 0$$. 4. **Calculate minimum value:** $$ f\left(\frac{1}{2}\right) = \left| \frac{1}{2} - \frac{1}{2} \right| - 2 = 0 - 2 = -2 $$ 5. **Range:** Since $$|x - \frac{1}{2}|$$ can grow without bound, $$f(x)$$ can take any value greater than or equal to $$-2$$. 6. **Answer:** The range is $$[-2, \infty)$$ which corresponds to option A. --- **Final answer:** A. $$[-2, \infty)$$