Solve the Problem $\mathrm { R } ( \mathrm { x } )$

question 17

Multiple Choice

Solve the problem.
-Determine which rational function $\mathrm { R } ( \mathrm { x } )$ has a graph that crosses the $x$ -axis at $- 1$ , touches the $x$ -axis at $- 4$ , has vertical asymptotes at $x = - 2$ and $x = 3$ , and has one horizontal asymptote at $y = - 2$ .

• A) \(R ( x ) = \frac { - 2 ( x + 1 ) ( x + 4 ) ^ { 2 } } { ( x + 2 ) ^ { 2 } ( x - 3 ) } , x \neq z - 2,3\)
• B) \(R ( x ) = \frac { - 2 ( x + 1 ) ( x + 4 ) } { ( x + 2 ) ( x - 3 ) } , x \neq - 2,3\)
• C) \(R ( x ) = \frac { - ( x + 1 ) ( x + 4 ) ^ { 2 } } { 2 ( x - 2 ) ^ { 2 } ( x + 3 ) } , x \neq 2 , - 3\)
• D) \(R ( x ) = \frac { - 2 ( x - 3 ) ( x + 2 ) ^ { 2 } } { ( x + 4 ) ^ { 2 } ( x + 1 ) } , x \neq - 4 , - 1\)

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Definitions:

Marginal Revenue

The additional income generated from selling one more unit of a good or service.

Total Revenue

Total Revenue is the full amount of income generated by the sale of goods or services before any costs are deducted.

Perfectly Elastic Demand

Demand in which quantity drops to zero at the slightest increase in price.

Ceteris Paribus

A Latin phrase meaning "all other things being equal," used in economics to analyze the effect of one variable change while holding others constant.