Question

What is the end behavior of the function f of x equals negative 2 times the cube root of x?

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

Answer 1

The end behavior of the function f(x) = -2√x is such that as x approaches infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) also approaches negative infinity.

Step-by-step explanation:

The function in question is f(x) = -2 √x, where √ represents the cube root. When considering the end behavior of this function, we need to examine what happens as x approaches negative infinity (x → ∞) and positive infinity (x → ∞). For large positive values of x, the cube root of x is also large and positive, but because of the negative coefficient (-2), f(x) becomes increasingly negative. As such, as x → ∞, f(x) → -∞. Conversely, for large negative values of x, the cube root of x becomes increasingly negative and so does f(x) due to the negative coefficient. Therefore, as x → -∞, f(x) → -∞ as well.

Answer 2

The end behavior of the function f(x) = -2∛x can be determined by looking at the highest degree term in the function, which is ∛x. Since the cube root of a negative number is also negative, as x approaches negative infinity, f(x) approaches negative infinity as well. Similarly, as x approaches positive infinity, f(x) approaches positive infinity. Therefore, the correct answer is:

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