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. It is determined by the degree of the polynomial and the sign of the leading coefficient.

Front

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

Back

The degree of a polynomial determines the number of times the graph can turn. Even-degree polynomials have the same end behavior on both sides, while odd-degree polynomials have opposite end behaviors.

Front

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

Back

The leading coefficient affects the direction of the ends of the graph. A positive leading coefficient means the ends of the graph rise to positive infinity, while a negative leading coefficient means the ends fall to negative infinity.

Front

Identify the end behavior of f(x) = -2x^3 + 4x + 1.

Back

As x → ∞, f(x) → -∞; As x → -∞, f(x) → ∞.

Front

Identify the end behavior of f(x) = 5x^4 - 3x^2 + 2.

Back

As x → ∞, f(x) → ∞; As x → -∞, f(x) → ∞.

Front

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

Back

As x → ∞, f(x) → -∞; As x → -∞, f(x) → -∞.

Front

How do you determine the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial.

Front

What is the degree of the polynomial f(x) = 4x^5 - 2x^3 + x?

Back

The degree of the polynomial is 5.

Front

What is the leading coefficient of the polynomial f(x) = -3x^4 + 2x^2 - 1?

Back

The leading coefficient is -3.

Front

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

Back

As x → ∞, f(x) → ∞; As x → -∞, f(x) → ∞.