Polynomial End Behavior

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

As x approaches -∞, what does f(x) approach for a polynomial with an odd degree and a positive leading coefficient?

Back

f(x) approaches -∞.

Front

As x approaches +∞, what does f(x) approach for a polynomial with an odd degree and a positive leading coefficient?

Back

f(x) approaches +∞.

Front

Back

The degree is 3.

Front

What is the degree of a polynomial function?

Back

The degree of a polynomial function is the highest power of the variable in the polynomial.

Front

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

Back

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches +∞.

Front

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

Back

As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) approaches -∞.

Front

What is the leading coefficient of a polynomial?

Back

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

Front

How does the sign of the leading coefficient affect the end behavior of a polynomial function?

Back

A positive leading coefficient will cause the function to rise to +∞ on both ends if the degree is even, and to +∞ on the right and -∞ on the left if the degree is odd.

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 behaviors.