1. **State the problem:** Find the limit $$\lim_{x \to \infty} -x^2 + 7x - 1$$. 2. **Recall the rule for limits at infinity of polynomials:** The term with the highest power dominates the behavior as $$x \to \infty$$. 3. **Identify the highest power term:** Here, the highest power term is $$-x^2$$. 4. **Evaluate the limit:** As $$x \to \infty$$, $$-x^2 \to -\infty$$, and the lower degree terms $$7x$$ and $$-1$$ become insignificant compared to $$-x^2$$. 5. **Conclusion:** Therefore, $$\lim_{x \to \infty} -x^2 + 7x - 1 = -\infty$$.