Question

What is the end behavior of f(x) = 4x4 - 3x² + 2?A. as a → ∞o, f(x) → ∞o as r→-∞, f(x) → -∞OB. as r→ ∞o, f(x) →-∞o as x→ -∞, f(x) →∞OC. as →∞o, f(x) → -∞o as a →-∞, f(x) →∞1OD. as a →∞o, f(x) →∞o as x→-∞, f(x) →∞Reset Selection

Answer 1

Explanation

To find the end behaviour of the function, we take the limit:

$\lim_{x\to\pm\infty}f(x)=\lim_{x\to\pm\infty}(4x^4-3x^2+2)=4\lim_{x\to\pm\infty}x^4=4\cdot\infty=\infty.$

Where we considered the dominant part of the polynomial to compute the limit.

Answer

D. As x → ∞, f(x) → ∞, as x → -∞, f(x) → ∞