Question

What is the end behavior of the function? f(x)=2x⁴+5x³-2x+12 Enter your answer by filling in the boxes.

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Answer 1

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

Final answer:

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

Step-by-step explanation:

The end behavior of a function refers to the behavior of the function as x approaches positive or negative infinity.

For the function f(x) = 2x⁴+5x³-2x+12, as x approaches negative infinity, the leading term 2x⁴ dominates the function. Since the degree of the leading term is even and the coefficient is positive, the end behavior is that f(x) approaches positive infinity.

As x approaches positive infinity, the leading term 2x⁴ still dominates the function, but this time the end behavior is that f(x) approaches positive infinity as well. So, the end behavior of the function f(x) = 2x⁴+5x³-2x+12 is that f(x) approaches positive infinity as x approaches both negative and positive infinity.