Question

Please help me determine the end behavior of the given polynomial function?: f(x) = 3x^5 - x^3 + 1/2

(A) As x -> ∞, f(x) -> ∞, and as x -> -∞, f(x) -> -∞
(B) As x -> ∞, f(x) -> -∞, and as x -> -∞, f(x) -> ∞
(C) As x -> ∞, f(x) -> -∞, and as x -> -∞, f(x) -> -∞
(D) As x -> ∞, f(x) -> ∞, and as x -> -∞, f(x) -> ∞

Answer 1

f(x) = 3x^5 - x^3 + 1/2 = x^3 (3x^2 - 1) + 1/2
Now the limit will only follow the sign of x^3 so :
When x -> ∞ then x^3 -> ∞ thus f(x) -> ∞
And when x -> -∞, then x^3 -> -∞ so f(x) -> -∞

Answer 2

so my answer's C? @math&ing001

Answer 3

Nope, try again
When x -> ∞ then f(x) -> ∞
And when x -> -∞, f(x) -> -∞

Answer 4

Ohhh so A? @math&ing001

Answer 5

i think so

Answer 6

Yep @JoeJoldin ! Sorry for the late response =)