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 the input values (x) approach positive or negative infinity.

Front

How does the leading coefficient of a polynomial affect its end behavior?

Back

The leading coefficient determines the direction of the end behavior: if it is positive, the function will rise to the right; if negative, it will fall to the right.

Front

What is the significance of the degree of a polynomial in determining end behavior?

Back

The degree of a polynomial indicates the highest power of x. It affects the end behavior: even degrees lead to the same direction at both ends, while odd degrees lead to opposite directions.

Front

For the polynomial f(x) = x^2 - 3x + 7x^9, what is the end behavior?

Back

The end behavior is DOWN as x approaches negative infinity and UP as x approaches positive infinity.

Front

For the polynomial f(x) = -5x^7, what is the end behavior?

Back

The end behavior is UP as x approaches negative infinity and DOWN as x approaches positive infinity.

Front

For the polynomial f(x) = -x^2 + 4x^4 + 9x^6 - 11x^5, what is the end behavior?

Back

The end behavior is UP as x approaches both negative and positive infinity.

Front

For the polynomial f(x) = -x^4, what is the end behavior?

Back

The end behavior is DOWN as x approaches both negative and positive infinity.

Front

For the polynomial f(x) = x^2, what is the end behavior?

Back

The end behavior is UP as x approaches both negative and positive infinity.

Front

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

Back

The end behavior will be UP as x approaches both negative and positive infinity.

Front

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

Back

The end behavior will be DOWN as x approaches negative infinity and UP as x approaches positive infinity.