Question

What is the end behavior of the function f of x equals negative 4 times the cube root of x?

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) → 0, and as x → ∞, f(x) → 0.
D.) As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.

Answer 1

B.) As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.

Explanation:

`\lim_(x\rightarrow -\infty ) f\left( x\right) =\lim_(x\rightarrow -\infty ) -4\sqrt[3]{x} = (-4)*(-\infty) = +\infty`

`\lim_(x\rightarrow \infty ) f\left( x\right) =\lim_(x\rightarrow \infty ) -4\sqrt[3]{x} = (-4)*(+\infty) = -\infty`