Overview of Multiplicity of a zero - Online Tutor - Free Math Videos

The video tutorial explains the concept of polynomial multiplicity and its impact on graphing. It covers how zeros can be expressed as factors and how multiplicity affects the graph's behavior at those zeros. The tutorial provides an example of graphing a polynomial, highlighting the importance of understanding end behavior and multiplicity. The video concludes with a review of these concepts, emphasizing their role in accurately graphing polynomial functions.

What does it mean when a polynomial factor is raised to a power?

• It indicates the degree of the polynomial.

• It represents the multiplicity of the zero.

• It determines the y-intercept of the graph.

• It shows the number of times the graph will cross the x-axis.

How does the multiplicity of a zero affect the graph at that point?

• The graph will always touch the y-axis.

• The graph will have a vertical asymptote.

• The graph will touch or cross the x-axis depending on whether the multiplicity is odd or even.

• The graph will always cross the x-axis.

What is the first step in graphing a polynomial function?

• Identifying the horizontal asymptotes.

• Calculating the derivative.

• Determining the end behavior using the leading coefficient test.

• Finding the y-intercept.

In the context of polynomial graphs, what does 'end behavior' refer to?

• The number of times the graph crosses the x-axis.

• The highest point on the graph.

• The direction the graph heads as x approaches positive or negative infinity.

• The slope of the tangent line at the origin.

When given a polynomial with a factor of (x + 3)^2, what can be inferred about the graph at x = -3?

• The graph will have a vertical asymptote at x = -3.

• The graph will have a hole at x = -3.

• The graph will cross the x-axis at x = -3.

• The graph will touch but not cross the x-axis at x = -3.