Final answer:
As x approaches infinity, the polynomial f(x) = 1 - 2x + 5x⁴ does not approach negative infinity.
Step-by-step explanation:
To determine whether the polynomial f(x) = 1 - 2x + 5x⁴, as x → ∞, approaches -∞, we need to consider the leading term of the polynomial. The leading term is the term with the highest exponent, in this case, 5x⁴. As x approaches infinity, the leading term dominates the polynomial, and the sign of the leading term determines the direction the polynomial approaches.
In this case, the coefficient of the leading term is positive (5), which means that as x approaches infinity, the polynomial also approaches positive infinity, not negative infinity. Therefore, the statement f(x) → -∞ as x → ∞ is False.