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

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

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

Sep 9, 2019

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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   Sep 9, 2019