Advanced Precalculus Unit 3 Flashcard Review

Front

What is the end behavior of a polynomial function with an odd degree and a negative leading coefficient?

Back

As x approaches infinity, the function approaches negative infinity, and as x approaches negative infinity, the function approaches positive infinity.

Front

What does a Local Minimum represent on a graph?

Back

A Local Minimum is a point where the function value is lower than all nearby points, indicating a local low point in the graph.

Front

How do you determine the number of extrema (maxima and minima) in a polynomial function's graph?

Back

Count the number of peaks (maxima) and valleys (minima) in the graph.

Front

Back

This expression indicates that the graph touches the x-axis at x = -3 and x = 2, creating a local minimum at these points.

Front

Back

@@ ext{As } x o ext{infinity, } f(x) o - ext{infinity}.$$

Front

What does the degree of a polynomial function indicate about its end behavior?

Back

The degree determines the direction of the ends of the graph: odd degrees have opposite ends, while even degrees have the same end behavior.

Front

What is the leading coefficient test for determining the end behavior of polynomial functions?

Back

The sign of the leading coefficient combined with the degree of the polynomial determines the end behavior.

Front

Define Absolute Maximum in the context of a function's graph.

Back

An Absolute Maximum is the highest point over the entire domain of the function.

Front

Define Absolute Minimum in the context of a function's graph.

Back

An Absolute Minimum is the lowest point over the entire domain of the function.

Front

What is a Local Maximum?

Back

A Local Maximum is a point where the function value is higher than all nearby points, indicating a local high point in the graph.