Question

Use the function f(x)

the questions below.
Match the correct end behavior.
2 Saved>
ƒ(x) = −x¹ − 5x³ + 12x² + 36x to answer
x →→[infinity], f(x) → _ 1. [infinity]
x →[infinity], f(x) → _
2. -[infinity]

Answer 1

The end behavior of the given function is (1) as x approaches negative infinity, f(x) approaches positive infinity, and (2) as x approaches positive infinity, f(x) approaches negative infinity.

Step-by-step explanation:

The end behavior of a function can be determined by looking at the leading term of the function. In the given function, f(x) = -x¹ - 5x³ + 12x² + 36x, the leading term is -x¹. Since the exponent of x is odd and the coefficient is negative, the end behavior of the function is as follows:

1. As x approaches negative infinity, f(x) approaches positive infinity.
2. As x approaches positive infinity, f(x) approaches negative infinity.