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How does the multiplicity of a zero affect the graph of the polynomial function?

Select answers from the choices  to correctly complete the statements.

The zeros of a seventh degree polynomial function are 1, 2 (multiplicity of 3), 4, and 6 (multiplicity of 2).

 

The graph of the function will cross through the x-axis at

 

a) 1 only b) 1 and 2 only c) 2 and 4 only d)1,2,and 4 only e) 2,4,and 6 only.

 

The graph will only touch (be tangent to) the x-axis at

a)1 only b)6 only c)2 and 4 only d)1,2,and 6 only e)2,4,and 6 only

.

At the zero of 2, the graph of the function will

a)cross through while hugging b)come close to but never touch c)cross striaght through 

 

the x-axis.

 

i think its A) and then C) and then b) ? I am honestly very confused

 Aug 28, 2019
 #1
avatar+103148 
+1

Well...one way to do this is just to graph this, here : https://www.desmos.com/calculator/qoifb2gezc

 

Note that all "odd" multiplicities of a zero will "cut" the x axis [or cross through while "hugging" ]   while all the "even" multiplicities  of a zero will "kiss" the x axis

 

So....for the first one  ...."d"  is true

 

For the second ...."b"  is true

 

For the last..we have one more thing that can happen with an "odd" multiplicity.."a" is true  because the zero at 2  is of an odd multiplicity > 1 .....[this will always happen when we have an "odd" multiplicity > 1 of a zero   ]

 

 

Hope that helps  !!!!

 

 

cool cool cool

 Aug 28, 2019

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