Question

Which describes the end behavior of the graph of the function f(x) = -8x⁴−2x³+x?

A.f(x)→[infinity] as x→−[infinity] and f(x)→[infinity] as x→[infinity]
B.f(x)→−[infinity] as x→−[infinity] and f(x)→−[infinity] as x→[infinity]
C.f(x)→[infinity] as x→−[infinity] and f(x)→−[infinity] as x→[infinity]
D.f(x)→−[infinity] as x→−[infinity] and f(x)→[infinity] as x→[infinity]

Answer 1

The end behavior of the graph of the function f(x) = -8x⁴ - 2x³ + x is that f(x) approaches positive infinity as x approaches negative infinity and approaches positive infinity as x approaches positive infinity.

Step-by-step explanation:

The end behavior of a function describes what happens to the function as x approaches positive or negative infinity. In the case of the function f(x) = -8x⁴ - 2x³ + x, the leading term is -8x⁴. Since the exponent of x is even and the coefficient is negative, the end behavior of the graph of the function is as follows:

• As x approaches negative infinity, f(x) approaches positive infinity.
• As x approaches positive infinity, f(x) also approaches positive infinity.

Therefore, the correct answer is (A) f(x)→[infinity] as x→−[infinity] and f(x)→[infinity] as x→[infinity].