What is the end behavior for the polynomial function

f(x)=−x6−9x+4

Question

What is the end behavior for the polynomial function

f(x)=−x6−9x+4

BlackTom AI · Accepted Answer

We start by identifying the key features of the polynomial. The function is f(x) = -x^6 - 9x + 4, where the highest-degree term is -x^6. The degree is even (6) and the leading coefficient is negative, which determines the end behavior: as x grows large in either the positive or negative direction, the dominant term -x^6 drives f(x) toward negative infinity. In other words, both ends go downward.

Since the provided answer options are not listed here (the answer_options field is empty), there is nothing to compare against. The standard rule for end behavior of even-degree polynomials with negative leading coefficient predicts f(x) → -∞ as x → ±∞, which corresponds to the description: Down to the left and down to the right.

If there were alternative choices, they would need to reflect either a different end behavior (e.g., up on one or both ends) or misinterpretation of the degree or leading coefficient. However, given the function's form, the correct interpretation is that both ends approach negative infinity, consistent with the identified end behavior.

ALGII141-027 4.9 Practice Problems

What is the end behavior for the polynomial function f(x)=−x6−9x+4

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