Polynomial Characteristics Check

Front

What is the domain of a polynomial function?

Back

The domain of a polynomial function is always (-∞, +∞).

Front

What is a relative minimum in a polynomial function?

Back

A relative minimum is a point where the function value is lower than all nearby points. For example, (-2.55, -6.55) and (2.55, -6.55) are relative minima.

Front

What does it mean if a polynomial has an even degree and a positive leading coefficient?

Back

It means that the ends of the graph of the polynomial will rise on both sides, and it will have a U-shaped appearance.

Front

When is a polynomial function decreasing?

Back

A polynomial function is decreasing on the interval (-1.5, 1.5).

Front

When is a polynomial function increasing?

Back

A polynomial function is increasing on the intervals (-∞, -1.5) and (1.5, ∞).

Front

What is the leading coefficient of a polynomial?

Back

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

Front

How can you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function can be determined by its degree and leading coefficient.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the maximum number of roots and the general shape of the graph.

Front

What are the characteristics of odd degree polynomials?

Back

Odd degree polynomials have opposite end behaviors; one end rises while the other falls.

Front

What are the characteristics of even degree polynomials?

Back

Even degree polynomials have the same end behavior; both ends either rise or fall.