Polynomial End Behavior

Front

What determines the end behavior of a polynomial function?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

If f(x) = 5x^4 - x + 6, what is the end behavior?

Back

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

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the 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 a leading coefficient?

Back

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

Front

What is the end behavior of a polynomial with degree 3?

Back

The end behavior can vary; if the leading coefficient is positive, it goes from -∞ to +∞, and if negative, it goes from +∞ to -∞.