Question

What is the end behavior of the function

f(x)=2x⁴−5x³−2x−12?

a) As x→−[infinity], f(x)→−[infinity];As x→−[infinity], f(x)→−[infinity]
b) As x→[infinity], f(x)→[infinity]; As x→−[infinity], f(x)→−[infinity]
c) As x→[infinity], f(x)→−[infinity]; As x→−[infinity], f(x)→[infinity]
d) As x→[infinity], f(x)→[infinity]; As x→−[infinity], f(x)→[infinity]

Answer 1

The end behavior of the function f(x) = 2x⁴ - 5x³ - 2x - 12 is that as x approaches negative or positive infinity, f(x) approaches positive infinity.

Step-by-step explanation:

The end behavior of a function is the way the function behaves as the input values (x) approach positive or negative infinity. To determine the end behavior of the function f(x) = 2x⁴ - 5x³ - 2x - 12, we look at the leading term of the polynomial, which is 2x⁴. Since the degree of the leading term is even and the coefficient is positive, the end behavior of the function is as follows:

As x approaches negative infinity, f(x) approaches positive infinity. This means that the function increases without bound as x gets smaller and smaller.

As x approaches positive infinity, f(x) also approaches positive infinity. This means that the function increases without bound as x gets larger and larger.