End Behavior

Front

What determines the end behavior of a polynomial function?

Back

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

Front

What is the leading coefficient of the polynomial 7x^5 - 9x^2 + 6x?

Back

The leading coefficient is 7.

Front

What is the degree of the polynomial 9x^5 + 2x^4 - x^3 + 9x^2 - 2?

Back

The degree is 5.

Front

In the end behavior of a polynomial function, what does it mean if the leading coefficient is positive and the degree is odd?

Back

As x approaches +∞, f(x) approaches +∞; as x approaches -∞, f(x) approaches -∞.

Front

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

Back

As x approaches +∞, f(x) approaches +∞; as x approaches -∞, f(x) approaches +∞.

Front

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

Back

As x approaches +∞, f(x) approaches -∞; as x approaches -∞, f(x) approaches +∞.

Front

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

Back

As x approaches +∞, f(x) approaches -∞; as x approaches -∞, f(x) approaches -∞.

Front

How can you identify the degree of a polynomial?

Back

The degree of a polynomial is identified by the highest exponent of the variable in the polynomial.

Front

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

Back

The leading coefficient affects the direction in which the polynomial function approaches infinity or negative infinity.

Front

If a polynomial has a degree of 3, what can you say about its end behavior?

Back

If the leading coefficient is positive, as x approaches +∞, f(x) approaches +∞; as x approaches -∞, f(x) approaches -∞.