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).