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How does the multiplicity of a zero determine the behavior of the graph at that zero? the drop down options are: is tangent to, crosses straight through, and crosses though while hugging

How Does The Multiplicity Of A Zero Determine The Behavior Of The Graph At That Zero The Drop Down Options Are Is Tangent To Crosses Straight Through And Crosse class=

Sagot :

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

Required: To determine the behavior of the graph at the zeros.

Explanation: The given seventh-degree polynomial can be represented as

[tex]\left(x+6\right)\left(x-0\right)^2\left(x-1\right)(x-4)^3[/tex]

Now, the graph will cross straight through at x=-6 and x=1.

We have an odd multiplicity at x=4; hence the graph will cross through while hugging.

We have an even multiplicity at x=0; therefore, the graph will be tangent.

Here is the graph of the given function-

Final Answer: The graph will cross straight through at x=-6 and x=1,

the graph will cross through while hugging at x=4,

the graph will be tangent at x=0.

View image TydariusK467189
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