What is the end behavior of f(x) = -x^4 + 2x^3 - x?

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Study for the Algebra 2 Honors Test. Prepare with flashcards and multiple choice questions, each question comes with hints and detailed explanations. Excel in your exam preparation!

Multiple Choice

What is the end behavior of f(x) = -x^4 + 2x^3 - x?

Explanation:
The end behavior of a polynomial is dictated by its leading term for large |x|. Here the leading term is -x^4, which has even degree and a negative coefficient. That means as x grows large in either direction, the x^4 term dominates and pulls the value toward negative infinity. So as x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞. The other terms (2x^3 and -x) become negligible in comparison for very large |x|, so they don’t change this trend. This explains why both ends head downward, not upward or oscillating.

The end behavior of a polynomial is dictated by its leading term for large |x|. Here the leading term is -x^4, which has even degree and a negative coefficient. That means as x grows large in either direction, the x^4 term dominates and pulls the value toward negative infinity. So as x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞. The other terms (2x^3 and -x) become negligible in comparison for very large |x|, so they don’t change this trend. This explains why both ends head downward, not upward or oscillating.

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