Graph Polynomials Effect of Multiplicity on a graph

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Presentation transcript:

Graph Polynomials Effect of Multiplicity on a graph

Multiplicity the graph curves as it crosses the x-axis. Multiplicity of a root is the number of times a root is a factor of a function. When a real root is singular the graph passes through the x-axis When a real root has even multiplicity the graph touches the x-axis but does NOT cross it. When a real root has odd multiplicity (3 or higher) the graph curves as it crosses the x-axis. The graph flattens as it approaches the x-axis when the multiplicity is higher.

Multiplicity--Factor and solve the following polynomial The root -3 has a multiplicity of 2. The graph touches at (-3, 0). The root 0 has a multiplicity of 3 The graph curves at (0, 0).

Example 2: State the zeros, approximate multiplicity, degree, leading coefficient, Domain, Range, End Behavior and Factors of the following graph. even

Example 3: State the zeros, approximate multiplicity, degree, leading coefficient, Domain, Range, End Behavior and Factors of the following graph. odd

Example 4 Find the roots for the function… X-2 IS A factor

Find the roots for the function… Example 5 Find the roots for the function… X-1 is a factor

Find the roots for the function… Example 6 Find the roots for the function… GCF Factors

Find the roots for the function… Example 7 Find the roots for the function… X+1 IS A factor