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A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?

The graph of the function is positive on (–6, –2).
The graph of the function is negative on (negative infinity, 0).
The graph of the function is positive on (–2, 4).
The graph of the function is negative on (4, infinity).

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mhanifa

Answer:

  • A. The graph of the function is positive on (–6, –2)

Step-by-step explanation:

The given function is an increasing function that intercepts the x- axis at -6, -2 and 4 and touches at 0.

It has minimum at negative infinity, maximum at positive infinity, local minimums between -2 and 0 and between 0 and 4, local maximum between -6 and -2.

Approximate shape is given in the attached.

Correct choice is the first one, the rest choices are all incorrect.

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