Polynomial End Behavior

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 (x) approach positive or negative infinity.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by its leading term, specifically the degree and the leading coefficient.

Front

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

Back

If the degree is even, both ends of the graph will either rise or fall together. If the degree is odd, one end will rise while the other falls.

Front

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

Back

Both ends of the graph will rise as x approaches positive or negative infinity.

Front

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

Back

Both ends of the graph will fall as x approaches positive or negative infinity.

Front

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

Back

The left end of the graph will fall while the right end will rise as x approaches negative infinity and positive infinity, respectively.

Front

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

Back

The left end of the graph will rise while the right end will fall as x approaches negative infinity and positive infinity, respectively.

Front

What is a leading term in a polynomial?

Back

The leading term is the term in a polynomial with the highest degree, which significantly influences the end behavior of the function.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the leading term, which determines the direction of the graph's end behavior.

Front

How can you identify the end behavior of a polynomial function from its graph?

Back

You can identify the end behavior by observing the direction in which the graph extends as x approaches positive and negative infinity.