End Behavior

Front

What is end behavior in functions?

Back

End behavior describes the behavior of a 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 have the same end behavior, while odd degrees have opposite end behavior.

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

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

Back

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

Front

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

Back

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

Front

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

Back

The left end of the graph falls to negative infinity, and the right end rises to positive infinity.

Front

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

Back

The left end of the graph rises to positive infinity, and the right end falls to negative infinity.

Front

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

Back

You can determine the end behavior by looking at the leading term of the polynomial.

Front

What is the degree of the polynomial -x^3 + 2x^2 + 3?

Back

The degree is 3, which is odd.

Front

What is the degree of the polynomial x^4 + 3x^3 - 4x + 1?

Back

The degree is 4, which is even.