Algebra 87 - Graphing Polynomial Functions - Part 2

The video tutorial explores polynomial functions, focusing on their characteristics, such as continuity and smoothness. It explains how to find zeros and X intercepts, emphasizing the role of factors and multiplicity in determining graph behavior. The tutorial guides viewers through sketching polynomial graphs, considering end behavior and turning points, and addresses special cases where standard techniques may not suffice.

What is a key characteristic of polynomial functions that allows their graphs to be drawn without lifting the pen?

• They are discrete.

• They are continuous.

• They have sharp corners.

• They are periodic.

What is the term used for the X values where a polynomial function equals zero?

• Roots

• Intercepts

• Extremes

• Zeros

How can the zeros of a polynomial function be found?

• By differentiating the function

• By integrating the function

• By using the Pythagorean theorem

• By factoring the polynomial into linear terms

What does a factor's multiplicity indicate about a polynomial's graph at an X intercept?

• The graph's color

• The graph's slope

• The graph's curvature

• The graph's behavior at the intercept

What happens at an X intercept with an odd multiplicity?

• The graph has a horizontal tangent.

• The graph has a vertical tangent.

• The graph crosses the X axis.

• The graph touches the X axis without crossing.

What determines the end behavior of a polynomial function?

• The leading term

• The degree of the polynomial

• The number of terms

• The constant term

How does the leading term's exponent affect a polynomial's end behavior?

• It influences the graph's growth direction.

• It affects the graph's symmetry.

• It changes the graph's periodicity.

• It determines the graph's color.

What is a turning point in the context of polynomial graphs?

• A point where the graph changes direction

• A point where the graph becomes linear

• A point where the graph crosses the X axis

• A point where the graph touches the Y axis

What is the maximum number of turning points a polynomial graph can have?

• Equal to the degree of the polynomial

• Half the degree of the polynomial

• One less than the degree of the polynomial

• Twice the degree of the polynomial

What should be done if a polynomial function has no X intercepts?

• Use a graphing utility

• Ignore the function

• Assume the graph is linear

• Calculate the function's value at various points