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 x approaches positive or negative infinity.

Front

What determines the end behavior of a polynomial function?

Back

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

Front

What does a positive leading coefficient indicate for even-degree polynomials?

Back

For even-degree polynomials with a positive leading coefficient, the end behavior is that both ends of the graph rise to positive infinity.

Front

What does a negative leading coefficient indicate for odd-degree polynomials?

Back

For odd-degree polynomials with a negative leading coefficient, the end behavior is that the left end of the graph rises to positive infinity while the right end falls to negative infinity.

Front

What is the degree of the polynomial -2x^7 + 2x^4 + 4?

Back

The degree of the polynomial is 7.

Front

Which direction does x → -∞ represent?

Back

x → -∞ represents the left direction on the graph.

Front

What is the end behavior of the polynomial function f(x) = 3x^8 + 3x^5 - 4x + 7?

Back

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

Front

What does the notation x → ∞ signify?

Back

x → ∞ signifies that x is approaching positive infinity.

Front

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

Back

Both ends of the graph will fall to negative infinity.

Front

What is the end behavior of the polynomial function f(x) = 4x^5 - 4x^4 + 2x^3 - 9?

Back

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