Question

Which statement BEST describes the end behavior of f(x) = 9 - 3x - 4x^4 + 2x^6?

a) f(x) approaches -[infinity] as x approaches [infinity], and f(x) approaches [infinity] as x approaches -[infinity]
b) f(x) approaches [infinity] as x approaches [infinity], and f(x) approaches -[infinity] as x approaches -[infinity]
c) f(x) approaches 0 as x approaches [infinity], and f(x) approaches 0 as x approaches -[infinity]
d) f(x) approaches -[infinity] as x approaches [infinity], and f(x) approaches -[infinity] as x approaches -[infinity]

Answer 1

The end behavior of the polynomial function f(x) = 9 - 3x - 4x^4 + 2x^6 is best described as approaching infinity as x approaches both positive and negative infinity, due to its leading term with an even power and a positive coefficient.

Step-by-step explanation:

To determine the end behavior of the function f(x) = 9 - 3x - 4x4 + 2x6, we need to look at the highest power term, which dictates the behavior as x approaches infinity. Since the leading term is 2x6, which is even-powered with a positive coefficient, we know as x approaches infinity or negative infinity, the function's value will approach infinity. Therefore, the statement that BEST describes the end behavior of the given function is b) f(x) approaches infinity as x approaches infinity, and f(x) approaches infinity as x approaches negative infinity.