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

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

Back

The degree of a polynomial determines the direction of the ends of the graph. Even degrees lead to both ends going in the same direction, while odd degrees lead to ends going in opposite directions.

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 right end of the graph rises; if negative, the right end falls.

Front

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

Back

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

Front

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

Back

The left end of the graph falls while the right end rises as x approaches negative and positive infinity, respectively.

Front

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

Back

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

Front

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

Back

The left end of the graph rises while the right end falls as x approaches negative and positive infinity, respectively.

Front

Identify the degree of the polynomial: 4x^5 - 2x^3 + 7.

Back

The degree is 5 (odd).

Front

Identify the degree of the polynomial: -3x^4 + 2x^2 - 1.

Back

The degree is 4 (even).