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

question 216

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.
-Crosses the $x$ -axis at $- 2,0$ , and 4 ; lies below the $x$ -axis between $- 2$ and 0 ; lies above the $x$ -axis between 0 and 4 .

• A) \(f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x\)
• B) \(f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 8 x\)
• C) \(f ( x ) = - x ^ { 3 } - 2 x ^ { 2 } + 8 x\)
• D) \(f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 8 x\)

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Definitions:

Prefrontal Cortex

The part of the brain located at the front of the frontal lobes, involved in complex behaviors, decision making, and moderating social behavior.

Executive Function

A set of cognitive processes including attentional control, inhibitory control, working memory, and cognitive flexibility, as well as reasoning, problem-solving, and planning.

Brain Region

An anatomically distinct area of the brain responsible for specific functions, such as the prefrontal cortex's role in decision-making.

Localization of Function

Localization of function is the concept that specific areas of the brain are responsible for particular physical or psychological functions.