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 function f(x) = -8x^4 - 2x^3 + x is f(x) -> infinity as x -> -infinity and f(x) -> infinity as x -> infinity.

Step-by-step explanation:

The end behavior of a function describes the behavior of the function as x approaches positive infinity and negative infinity. To determine the end behavior of the function f(x) = -8x^4 - 2x^3 + x, we can look at the leading term, which is -8x^4. Since the leading term has an even degree and a negative coefficient, the end behavior 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 option is a. f(x) → ∞ as x → -∞ and f(x) → ∞ as x → ∞.