Polynomial Characteristics Check

Front

What are turning points in a polynomial function?

Back

Turning points are points on the graph where the function changes direction from increasing to decreasing or vice versa. They correspond to relative maximums and minimums.

Front

What is the domain of a polynomial function?

Back

The domain of a polynomial function is always (-∞, +∞), meaning it includes all real numbers.

Front

How do you determine the number of extrema in a polynomial function?

Back

The number of extrema (maximums and minimums) can be found by analyzing the turning points of the graph, which are where the derivative equals zero.

Front

What are x-intercepts of a polynomial function?

Back

X-intercepts are the points where the graph of the polynomial crosses the x-axis, meaning the function value is zero at those points.

Front

How do you find the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is a relative maximum?

Back

A relative maximum is a point on the graph of a function where the function value is higher than the values of the function at nearby points.

Front

What is a relative minimum?

Back

A relative minimum is a point on the graph of a function where the function value is lower than the values of the function at nearby points.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function. If it's positive, the graph rises to the right; if negative, it falls to the right.

Front

What is the relationship between the degree of a polynomial and the number of turning points?

Back

A polynomial of degree n can have at most n-1 turning points.

Front

What does it mean for a polynomial to be even or odd?

Back

An even polynomial has all even-degree terms and is symmetric about the y-axis. An odd polynomial has all odd-degree terms and is symmetric about the origin.