Polynomial Functions & End Behavior

Front

What is a polynomial function?

Back

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the end behavior of the polynomial function.

Front

How does the sign of the leading coefficient affect end behavior?

Back

If the leading coefficient is positive, the polynomial will rise to the right. If it is negative, the polynomial will fall to the right.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression. It indicates the polynomial's behavior and the number of roots.

Front

Back

Quartic (degree 4)

Front

What is a cubic function?

Back

Front

What is the standard form of a cubic function?

Back

Front

What is the difference between a linear and a quadratic function?

Back

Front

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

Back

The end behavior will rise on both ends (as x approaches positive or negative infinity, f(x) approaches positive infinity).

Front

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

Back

The end behavior will fall on the right and rise on the left (as x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches positive infinity).