End Behavior of Polynomials

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior is determined by the degree of the polynomial and the sign of the leading coefficient.

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How does the degree of a polynomial affect its end behavior?

Back

Even-degree polynomials have the same end behavior on both sides, while odd-degree polynomials have opposite end behavior.

Front

What is the end behavior of a polynomial with a positive leading coefficient and an even degree?

Back

As x approaches positive or negative infinity, the function approaches positive infinity.

Front

What is the end behavior of a polynomial with a negative leading coefficient and an even degree?

Back

As x approaches positive or negative infinity, the function approaches negative infinity.

Front

What is the end behavior of a polynomial with a positive leading coefficient and an odd degree?

Back

As x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches positive infinity.

Front

What is the end behavior of a polynomial with a negative leading coefficient and an odd degree?

Back

As x approaches negative infinity, the function approaches positive infinity, and as x approaches positive infinity, the function approaches negative infinity.

Front

Given the polynomial f(x) = -2x^7 + 2x^4 + 4, what is its leading coefficient?

Back

The leading coefficient is -2.

Front

Given the polynomial f(x) = 3x^8 + 3x^5 - 4x + 7, what is its degree?

Back

The degree of the polynomial is 8.