End Behavior, Inc/Dec, Max/Min

Front

What is end behavior in polynomial functions?

Back

End behavior describes the behavior of a polynomial function as x approaches positive or negative infinity.

Front

How does the leading coefficient affect the end behavior of a polynomial function?

Back

The sign of the leading coefficient determines whether the ends of the graph rise or fall: Positive leading coefficient means the ends rise, Negative means the ends fall.

Front

What does it mean for a polynomial to be increasing?

Back

A polynomial is increasing on an interval if the function values rise as x values increase.

Front

What does it mean for a polynomial to be decreasing?

Back

A polynomial is decreasing on an interval if the function values fall as x values increase.

Front

What is a local maximum in a polynomial function?

Back

A local maximum is a point where the function value is higher than all nearby points.

Front

What is a local minimum in a polynomial function?

Back

A local minimum is a point where the function value is lower than all nearby points.

Front

How can you determine the intervals of increase and decrease from a graph?

Back

By analyzing the slope of the graph: if the slope is positive, the function is increasing; if negative, it is decreasing.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of x and affects the end behavior and the number of turning points.

Front

What is the difference between odd and even degree polynomials?

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 leading term of a polynomial?

Back

The leading term is the term in a polynomial with the highest degree, which determines the end behavior.