Polynomial Functions and Their Properties

The video tutorial covers the characteristics of polynomials, focusing on terminology such as absolute and local maxima and minima. It explains how to describe end behavior, when a function is above or below the x-axis, and when it is increasing or decreasing. The tutorial includes practice problems and reviews answers to reinforce understanding of these concepts.

What is a turning point in the context of polynomials?

• A point where the graph intersects the x-axis

• A point where the graph changes direction

• A point where the graph reaches its highest value

• A point where the graph is horizontal

What is an absolute maximum?

• The highest point on the graph

• A point where the graph is horizontal

• A point where the graph changes direction

• The lowest point on the graph

What is the difference between a local maximum and an absolute maximum?

• An absolute maximum is a point where the graph changes direction

• An absolute maximum is the highest point on the graph

• A local maximum is the highest point on the graph

• A local maximum is a point where the graph changes direction

Which of the following is NOT an objective for describing polynomial characteristics?

• Describing end behavior

• Identifying turning points

• Determining intervals of increase and decrease

• Calculating the derivative

What does it mean when f(x) approaches positive infinity as x approaches positive infinity?

• The graph is going down

• The graph is going up

• The graph is horizontal

• The graph is at a turning point

When is a polynomial function considered to be above the x-axis?

• When f(x) is at a turning point

• When f(x) is greater than zero

• When f(x) is equal to zero

• When f(x) is less than zero

In which interval is the polynomial function increasing?

• Where the slope is undefined

• Where the slope is positive

• Where the slope is negative

• Where the slope is zero

What is the end behavior of a polynomial if both ends approach negative infinity?

• The graph is oscillating

• The graph is decreasing

• The graph is constant

• The graph is increasing

If a polynomial never crosses the x-axis, what can be said about its values?

• It is sometimes positive

• It is sometimes negative

• It is always positive

• It is always negative

What does it mean for a polynomial to be decreasing between two points?

• The slope is positive

• The slope is undefined

• The slope is zero

• The slope is negative