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) \(R ( x ) = \frac { - 2 ( x - 3 ) ( x + 2 ) ^ { 2 } } { ( x + 4 ) ^ { 2 } ( x + 1 ) } , x \neq - 4 , - 1\)

---

Definitions:

Charles I

King of England, Scotland, and Ireland from 1625 until his execution in 1649, whose reign was marked by religious and political strife leading to the English Civil War.

King Philip's War

A conflict between Native American inhabitants of New England and English colonists and their Native allies from 1675–1678, marked as one of the earliest and bloodiest conflicts in Colonial America.

Bacon's Rebellion

A 1676 armed rebellion led by Nathaniel Bacon against the colonial government of Virginia, sparked by grievances over governance and Native American policies.

Anglican Church

Also known as the Church of England, an independent Christian church which emerged during the Protestant Reformation, characterized by a middle path ('via media') between Roman Catholicism and Protestantism.