End Behavior

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 does it mean for a polynomial to have an odd degree?

Back

A polynomial with an odd degree will have end behavior where one end goes to positive infinity and the other end goes to negative infinity.

Front

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

Back

The end behavior will be down/down, meaning both ends of the graph will approach negative infinity.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior can be determined by the leading term of the polynomial, specifically its degree and leading coefficient.

Front

What is the end behavior of the function h(x) = -8x^5 + 22x^4 - 4x^3 + 11x - 9?

Back

The end behavior is up/down, meaning as x approaches negative infinity, h(x) approaches positive infinity, and as x approaches positive infinity, h(x) approaches negative infinity.

Front

What is the end behavior of the function g(x) = -2x^6 + 2x^5 - 12x - 6?

Back

The end behavior is down/down, meaning both ends of the graph approach negative infinity.

Front

What does it mean when a polynomial function approaches -∞ as x approaches -∞?

Back

It indicates that the left end of the graph goes down indefinitely.

Front

What does it mean when a polynomial function approaches +∞ as x approaches +∞?

Back

It indicates that the right end of the graph goes up indefinitely.

Front

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

Back

The leading coefficient determines whether the ends of the graph will rise or fall; a positive leading coefficient means the right end rises, while a negative leading coefficient means the right end falls.

Front

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

Back

The end behavior will be up/up, meaning both ends of the graph approach positive infinity.