What is the end behavior of the function f(x) = 3x⁴ - x³ + 2x² + 4x + 5?

Solution:

In order to determine the end behavior,

2 items have to be considered.

1. Degree of polynomial -

The degree is found by the highest exponent.

In the question, the degree is even, 4.

As the degree is even, both ends extend to positive infinity or negative infinity.

2. Second item finds if those end behaviours are positive or negative.

We now see the coefficient of term with highest degree.

In the question, the coefficient is positive 3.

If the coefficient is positive then the end behaviors are positive and if the coefficient is negative the end behavior is negative.

In the question, the end behaviors are ↑ and ↑.

Therefore, the end behaviors are ↑ and ↑.

What is the end behavior of the function f(x) = 3x⁴ - x³ + 2x² + 4x + 5?

Summary:

The end behavior of the function f(x) = 3x⁴ - x³ + 2x² + 4x + 5 are ↑ and ↑.