Solve the Problem $R ( x )$ Has a Graph That Crosses The

question 321

Multiple Choice

Solve the problem.
-Determine which rational function $R ( x )$ 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) \(R ( x ) = \frac { - 2 ( x + 1 ) ( x + 4 ) ^ { 2 } } { ( x + 2 ) ^ { 2 } ( x - 3 ) } , x \neq - 2,3\)
• 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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