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

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

Front

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

Back

For even-degree polynomials with a negative leading coefficient, the end behavior is: as x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞.

Front

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

Back

For odd-degree polynomials with a positive leading coefficient, the end behavior is: as x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

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

Front

If a polynomial has a degree of 4 and a leading coefficient of 3, what is its end behavior?

Back

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

Front

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

Back

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

Front

Describe the end behavior of the polynomial f(x) = x^3 - 4x + 1.

Back

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

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of x and influences the end behavior of the function.