End Behavior of Polynomials

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity.

Front

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

Back

The degree of a polynomial determines the number of times the graph can turn, influencing whether the ends of the graph go up or down.

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.

Front

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

Back

If the leading coefficient is positive, the graph will rise to the right; if negative, it will fall to the right.

Front

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

Back

Both ends of the graph will rise (up, up).

Front

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

Back

Both ends of the graph will fall (down, down).

Front

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

Back

The left end of the graph will fall and the right end will rise (down, up).

Front

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

Back

The left end of the graph will rise and the right end will fall (up, down).

Front

If a polynomial function has a degree of 4, what can be said about its end behavior?

Back

It will have the same end behavior as a polynomial with an even degree.

Front

What does it mean for a polynomial to have a degree of 3?

Back

It means the highest exponent of the variable in the polynomial is 3, indicating it is an odd degree polynomial.