Question

State the degree and end behavior of the following polynomial function:

f(x) = 3x³ + 2x⁴ + 1x² +1
Explain or show your reasoning.

Answer 1

The degree of the polynomial is 4 and the end behavior is that as x approaches positive infinity or negative infinity, the function approaches positive infinity.

Step-by-step explanation:

The given polynomial function is f(x) = 3x³ + 2x⁴ + 1x² + 1.

To determine the degree of the polynomial, we look at the term with the highest exponent. In this case, the term with the highest exponent is 2x⁴, so the degree of the polynomial is 4.

As for the end behavior, we observe the behavior of the polynomial as x approaches positive infinity and negative infinity. Since the leading term of the polynomial has an even degree and a positive coefficient (2x⁴), the end behavior is as follows:

• As x approaches positive infinity, the function f(x) approaches positive infinity.
• As x approaches negative infinity, the function f(x) also approaches positive infinity.