End Behavior of Polynomials

Front

What determines the end behavior of a polynomial function?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

Identify the leading coefficient and degree of the polynomial f(x) = 3x^4 - 5x^2 + 2.

Back

Leading Coefficient: 3 (positive), Degree: 4 (even).

Front

Identify the leading coefficient and degree of the polynomial f(x) = -2x^5 + 4x^3 - x.

Back

Leading Coefficient: -2 (negative), Degree: 5 (odd).

Front

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

Back

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

Front

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

Back

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

Front

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

Back

The sign of the leading coefficient indicates whether the ends of the graph rise or fall.