End Behavior of Polynomials

Front

What is the end behavior of a polynomial?

Back

The end behavior of a polynomial describes how the graph behaves as x approaches positive or negative infinity.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior is determined by the leading term of the polynomial, specifically its degree and the sign of its leading coefficient.

Front

If a polynomial has an even degree and a positive leading coefficient, what is its end behavior?

Back

The end behavior is up, up (as x approaches -∞, f(x) approaches +∞ and as x approaches +∞, f(x) approaches +∞).

Front

If a polynomial has an odd degree and a positive leading coefficient, what is its end behavior?

Back

The end behavior is down, up (as x approaches -∞, f(x) approaches -∞ and as x approaches +∞, f(x) approaches +∞).

Front

If a polynomial has an even degree and a negative leading coefficient, what is its end behavior?

Back

The end behavior is down, down (as x approaches -∞, f(x) approaches -∞ and as x approaches +∞, f(x) approaches -∞).

Front

If a polynomial has an odd degree and a negative leading coefficient, what is its end behavior?

Back

The end behavior is up, down (as x approaches -∞, f(x) approaches +∞ and as x approaches +∞, f(x) approaches -∞).

Front

What is the leading term of the polynomial f(x) = -3x^5 + 5x^4 - 7x^3 + 2x - 12?

Back

The leading term is -3x^5.

Front

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

Back

The degree determines whether the ends of the graph go in the same direction (even degree) or in opposite directions (odd degree).

Front

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

Back

The leading coefficient indicates the direction of the ends of the graph: positive means the ends go up, negative means the ends go down.

Front

Describe the end behavior of the polynomial f(x) = 4 + 3x - 6x^7 + 3x^4.

Back

The end behavior is up, down (as x approaches -∞, f(x) approaches -∞ and as x approaches +∞, f(x) approaches +∞).