End Behavior

Front

What is end behavior in polynomial functions?

Back

End behavior describes the behavior of the graph of a polynomial function as the input values (x) approach positive or negative infinity.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior is determined by the degree and the leading coefficient of the polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

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

Back

If the degree is odd, the ends of the graph will go in opposite directions. If the degree is even, the ends will go in the same direction.

Front

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

Back

As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches negative infinity.

Front

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

Back

As x approaches positive infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches positive infinity.

Front

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

Back

As x approaches both positive and negative infinity, f(x) approaches positive infinity.

Front

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

Back

As x approaches both positive and negative infinity, f(x) approaches negative infinity.

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 heads as x moves towards positive and negative infinity.