Question

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?

As x approaches negative infinity, y approaches positive infinity. As x approaches positive infinity, y approaches negative infinity.
As x approaches negative infinity, y approaches positive infinity. As x approaches positive infinity, y approaches positive infinity.
As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches negative infinity.
As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches positive infinity.

Answer 1

As x → −∞, y → +∞. As x → +∞, y → −∞.

Reason: the leading term is −x^3 (odd degree, negative leading coefficient), so the left end rises and the right end falls; equivalently −x^3 → +∞ as x → −∞ and −x^3 → −∞ as x → +∞.