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