3.3.4 End Behavior and Multiplicity

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the degree of the polynomial 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 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 positive infinity, the function approaches positive infinity, and as x approaches negative infinity, the function approaches negative infinity.

Front

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

Back

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

Front

Identify the degree and leading coefficient of the polynomial f(x) = 2x^3 - 5x + 1.

Back

Degree: 3 (odd), Leading Coefficient: 2 (positive).

Front

Identify the degree and leading coefficient of the polynomial f(x) = -4x^6 + 3x^2 - 2.

Back

Degree: 6 (even), Leading Coefficient: -4 (negative).

Front

Which polynomial has the end behavior where both ends go up?

Back

A polynomial with an even degree and a positive leading coefficient.

Front

Which polynomial has the end behavior where the left end goes up and the right end goes down?

Back

A polynomial with an odd degree and a positive leading coefficient.

Front

What is the significance of the leading coefficient in determining end behavior?

Back

The leading coefficient determines whether the ends of the polynomial function rise or fall as x approaches positive or negative infinity.