Polynomial Functions: End Behavior; Number of possible Zeros

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as the input values approach positive or negative infinity. It is determined by the leading term of the polynomial.

Front

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

Back

The degree of a polynomial determines the direction of the ends of the graph. If the degree is even, both ends will go in the same direction (either up or down). If the degree is odd, the ends will go in opposite directions.

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 influences the end behavior of the polynomial.

Front

Describe the end behavior of a polynomial with an even degree and a positive leading coefficient.

Back

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

Front

Describe the end behavior of a polynomial with an even degree and a negative leading coefficient.

Back

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

Front

Describe the end behavior of a polynomial with an odd degree and a positive leading coefficient.

Back

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

Front

Describe the end behavior of a polynomial with an odd degree and a negative leading coefficient.

Back

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

Front

What is the maximum number of real zeros a polynomial can have?

Back

A polynomial of degree n can have at most n real zeros.

Front

If a polynomial has a degree of 6, what is the maximum number of possible real zeros?

Back

The maximum number of possible real zeros is 6.

Front

What is the relationship between the degree of a polynomial and the number of turning points?

Back

A polynomial of degree n can have at most n-1 turning points.