1. Problem: Find the domain and range of $f(x) = x^2 - 4x + 1$. 2. Formula: Quadratic function $f(x) = ax^2 + bx + c$ with $a=1$, $b=-4$, $c=1$. 3. Domain: All real numbers, $\mathbb{R}$. 4. Find vertex: $x = -\frac{b}{2a} = -\frac{-4}{2 \times 1} = 2$. 5. Calculate $f(2) = 2^2 - 4 \times 2 + 1 = 4 - 8 + 1 = -3$. 6. Since $a=1 > 0$, parabola opens upwards, so range is $[-3, \infty)$. Final answer: Domain: $(-\infty, \infty)$, Range: $[-3, \infty)$