End Behavior of Polynomials

Front

What is the end behavior of the polynomial function f(x) = -7x^3 + 2x - 1 as x approaches infinity?

Back

As x → ∞, f(x) → -∞.

Front

What is the end behavior of the polynomial function f(x) = -7x^3 + 2x - 1 as x approaches negative infinity?

Back

As x → -∞, f(x) → ∞.

Front

What does x → -∞ represent in terms of graphing?

Back

It represents the left side of the graph.

Front

Complete the end behavior: As x → -∞, f(x) → ____ for the polynomial that approaches +∞ as x approaches both ends.

Back

+∞.

Front

Complete the end behavior: As x → +∞, f(x) → ____ for the polynomial that approaches +∞ as x approaches both ends.

Back

+∞.

Front

What determines the end behavior of a polynomial function?

Back

The degree and the sign of the leading coefficient.

Front

What is the degree of the polynomial function f(x) = -7x^3 + 2x - 1?

Back

The degree is 3 (odd).

Front

What is the sign of the leading coefficient in the polynomial function f(x) = -7x^3 + 2x - 1?

Back

The leading coefficient is negative.

Front

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

Back

Odd degree polynomials have opposite end behaviors; even degree polynomials have the same end behavior.

Front

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

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.