End Behavior Polynomials and relative extrema

Front

What is the leading coefficient of a polynomial?

Back

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

Front

What does the end behavior of a polynomial function describe?

Back

The end behavior describes how the values of the function behave as x approaches positive or negative infinity.

Front

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

Back

The degree determines the number of times the graph can turn, influencing whether it rises or falls at the ends.

Front

What is the difference between an odd and even degree polynomial in terms of end behavior?

Back

Odd degree polynomials have opposite end behaviors (one end rises, the other falls), while even degree polynomials have the same end behavior (both ends rise or both fall).

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 odd degree?

Back

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

Front

How can you determine the end behavior of the polynomial y = -2x^5 + 3x^3 - x + 1?

Back

Since the leading coefficient is negative and the degree is odd, as x -> -∞, f(x) -> ∞ and as x -> ∞, f(x) -> -∞.

Front

What is the degree of the polynomial y = 4x^6 - 2x^4 + 3?

Back

The degree is 6, which is even.

Front

Identify the leading coefficient of the polynomial y = 5x^3 - 4x + 2.

Back

The leading coefficient is 5.

Front

What is the end behavior of the polynomial y = x^4 - 3x^2 + 2?

Back

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