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Write an equation for a rational function with the given characteristics.Vertical asymptotes at x = -2 and x = 4, x-intercepts at (-3,0) and (1,0), horizontal asymptote at y = -2y =Additional MaterialseBookFind the Equation of a Rational FunctionExample Video

User Loz
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1 Answer

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Given:

The characteristics of rational function:

Vertical asymptotes at x = -2 and x = 4

x-intercepts at (-3,0) and (1,0).

horizontal asymptote at y = -2

The foem of rational function is,


(f(x))/(g(x))

For the vertical asymtotes x = -2 and x = 4, That means denominator will have the terms,


\begin{gathered} x=-2,x=4 \\ (x+2),(x-4) \end{gathered}

For x intercept (-3,0) and (1,0) , the terms on the numerator is,


\begin{gathered} (x+3)\text{ and (x-1)} \\ \text{Because this factors will given the values as x=-3 and x=1} \end{gathered}

So, the rational function becomes,


(f(x))/(g(x))=a((x+3)(x-1))/((x+2)(x-4))

The horizontal asymtoes will describes the functions behaviour when x approaches to infinity.

So, a=-2.


(f(x))/(g(x))=-2((x+3)(x-1))/((x+2)(x-4))

Answer:


(-2(x+3)(x-1))/((x+2)(x-4))

User MatFiz
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