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How does the multiplicity of a zero determine the behavior of the graph at that zero? Select answers from the drop down menu to correctly complete the statement. A seventh degree polynomial has zeros of -6,0(multiplicity of 3), 1 (multiplicity of 2), and 4

User Bhilstrom
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The graph of the function is tangent to the x-axis at -6.

The graph of the function crosses straight through the x-axis at 0.

The graph of the function crosses through while hugging the x-axis at 1.

The graph of the function crosses straight through the x-axis at 4.

How does the multiplicity of a zero determine the behavior of the graph at that zero

The multiplicity of a zero determines the behavior of the graph at that zero by indicating how many times the function changes sign at that point.

A zero with an even multiplicity means that the function changes sign twice at that point

This results in the graph touching and bouncing off the x-axis.

A zero with an odd multiplicity means that the function changes sign once at that point

This results in the graph crossing the x-axis.

The multiplicity of 3 at zero implies that the graph approaches zero but does not touch it, resembling a curve that hugs the x-axis.

Question

How does the multiplicity of a zero determine the behavior of the graph at that zero?

Select answers form the drop-down menus to correctly complete the statements.

A seventh degree polynomial function has zeros of −6 , 0 (multiplicity of 3), 1 (multiplicity of 2), and 4.

The graph of the function ( ) the x-axis at −6 .

The graph of the function ( )the x-axis at 0.

The graph of the function ( ) the x-axis at 1.

The graph of the function ( )the x-axis at 4.

The options for all the slots are either (is tagent to),(cross straight through), and (cross through while hugging).

User Pentzzsolt
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