Sketch the graph of the polynomial by hand using zeros, multiplicity and end behavior

The video tutorial covers finding zeros and their multiplicities for a polynomial function, and how these affect the graph's behavior. The instructor explains the process of setting the function to zero, solving for x, and determining multiplicity. The tutorial also discusses how to graph the function by considering zeros, multiplicity, and end behavior, using a step-by-step approach without graphing technology.

What is the first step in finding the zeros of a polynomial function?

• Find the derivative of the function

• Use a graphing calculator

• Factor the polynomial completely

• Set the function equal to zero

How does the graph behave at a zero with an odd multiplicity?

• It remains constant

• It crosses the x-axis

• It bounces off the x-axis

• It forms a vertical asymptote

What is a common misconception about even multiplicity?

• It is determined by the coefficient

• It always results in a crossing

• It is the same as odd multiplicity

• It is determined by the power of the factor

What does the leading coefficient test help determine?

• The multiplicity of each zero

• The zeros of the polynomial

• The symmetry of the graph

• The end behavior of the graph

If a polynomial has a degree of 5 and a positive leading coefficient, how does the graph behave?

• Rises left, falls right

• Falls left, rises right

• Rises left, rises right

• Falls left, falls right