92392
AssignmentMultiple Choice

The Cubing Function

Question 92392 • (OC27) MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006P

The function f(x) = –x3 + 2x2 – x + 5 is graphed on a coordinate grid. Which statements accurately describe the end behavior of the graph of the function?

Answer
A
As x approaches negative infinity, y approaches positive infinity. As x approaches positive infinity, y approaches negative infinity.
B
As x approaches negative infinity, y approaches positive infinity. As x approaches positive infinity, y approaches positive infinity.
C
As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches negative infinity.
D
As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches positive infinity.

Explanation

The end behavior is determined by the leading term, −x³, because it grows faster than the other terms. As x approaches negative infinity, −x³ approaches positive infinity; as x approaches positive infinity, −x³ approaches negative infinity. Therefore, the graph rises to the left and falls to the right, matching the statement in choice A.

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