Write the Equation of a Polynomial Function with the Given $x$

question 215

Multiple Choice

Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make
the degree of the function as small as possible.
-Touches the $x$ -axis at 0 and crosses the $x$ -axis at 3 ; lies below the $x$ -axis between 0 and 3 .

• A) \(f ( x ) = x ^ { 3 } - 3 x ^ { 2 }\)
• B) \(f ( x ) = - x ^ { 3 } + 3 x ^ { 2 }\)
• C) \(f ( x ) = - x ^ { 3 } - 3 x ^ { 2 }\)
• D) \(f ( x ) = x ^ { 3 } + 3 x ^ { 2 }\)

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Definitions:

Nonexcludable

A characteristic of public goods where it is not feasible to exclude individuals from using the good, leading to potential free-rider problems.

Common Resource

A resource, like air or water, that is accessible to all members of a society but subject to overuse and depletion.

Negative Externalities

Costs suffered by a third party due to an economic transaction they were not involved in.

Public Goods

Goods that are non-excludable and non-rivalrous, meaning individuals cannot be effectively excluded from use and where use by one individual does not reduce availability to others.