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).

I know this is quite a bit, but i really need some help on this

jjennylove Sep 9, 2019

#1**+1 **

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

The graph will cross straight through at x = -6 and x = 4

We have an odd multiplicity > 1 at x = 0......therefore.....the graph will "cross through while hugging" here [ this will always be true with an odd multiplicity > 1 ]

We have an even multiplicity at x = 1......the graph will always be tangent with an even multiplicity

Here's the graph : https://www.desmos.com/calculator/vpimkckn3k

CPhill Sep 9, 2019