Determining End Behavior of Graphs by Analyzing Equations

This video tutorial explains how to determine the end behavior of graphs by analyzing their equations. It covers power functions, focusing on even and odd exponents, and discusses how these affect graph shapes. The tutorial also explains how to identify increasing and decreasing functions on specific intervals. A significant portion is dedicated to understanding the end behavior of polynomials, emphasizing the importance of the lead term. The video concludes with practical examples of analyzing polynomial end behavior.

What happens to the graph of a power function as the exponent increases, specifically for even exponents?

• The graph becomes steeper and flatter around zero.

• The graph becomes a straight line.

• The graph becomes wider and less steep.

• The graph remains unchanged.

How can you tell if a function is increasing on an interval?

• Y goes to infinity as X goes to infinity.

• Y remains constant as X changes.

• Y goes to zero as X goes to infinity.

• Y goes to negative infinity as X goes to infinity.

What is the primary concern when analyzing the end behavior of polynomials?

• The middle terms of the polynomial.

• The lead term of the polynomial.

• The polynomial's degree.

• The constant term of the polynomial.

For a polynomial with an odd degree and a positive lead coefficient, what is the end behavior?

• Decreases on the left and increases on the right.

• Increases on both sides.

• Decreases on both sides.

• Increases on the left and decreases on the right.

How should you interpret a graph with a negative lead coefficient and an even degree?

• The graph increases on both sides.

• The graph decreases on both sides.

• The graph decreases on the left and increases on the right.

• The graph increases on the left and decreases on the right.

What is a common misunderstanding when interpreting the direction of a graph?

• Assuming the graph is always increasing.

• Assuming the graph is a straight line.

• Assuming the graph goes up on the left and down on the right based on arrow direction.

• Assuming the graph is always decreasing.

What is the correct interpretation of a graph that increases on both the far left and far right?

• The graph is decreasing overall.

• The graph is a parabola.

• The graph is constant.

• The graph is increasing overall.