Question

Given g(x) = -13x^2 – 10x^2 – 2x^6 – 14x, what is the end behavior of the function?

a) As x → [infinity], g(x) → -[infinity]; As x → -[infinity], g(x) → -[infinity]
b) As x → [infinity], g(x) → [infinity]; As x → -[infinity], g(x) → [infinity]
c) As x → [infinity], g(x) → -[infinity]; As x → -[infinity], g(x) → [infinity]
d) As x → [infinity], g(x) → [infinity]; As x → -[infinity], g(x) → -[infinity]

Answer 1

The end behavior of the function g(x) is dictated by the leading term, which is -2x^6. As x approaches either positive or negative infinity, g(x) will approach negative infinity.

Step-by-step explanation:

The end behavior of a function is determined by its highest power term. In the given function g(x) = -13x^2 – 10x^2 – 2x^6 – 14x, -2x^6 is the term with the highest degree. Therefore, the leading term, -2x^6, will dictate the end behavior of the function. As x approaches positive or negative infinity, the negative sign in front of the x^6 term means that the function will tend towards negative infinity in both directions. This means the correct end behavior for g(x) is that as x approaches infinity, g(x) approaches negative infinity, and as x approaches negative infinity, g(x) also approaches negative infinity.