Question

Use the given graph to create the equation for the rational function. The function is written in factored form to help you see how the given information shapes our equation.vert asymp at x=-3 opposite end behavior, vert asymp at x=2 same end behavior, bounce off x axis at x=1, y int at -1/2The numerator is: Answer (x-Answer)^2 The denominator is: (x+Answer )(x-Answer )(x-Answer )

Answer 1

Solution

The function is written in factored form

Using vertical asymptote at x = 3 opposite end behaviour

vert asymp at x=2 same end behavior, bounce off x axis at x=1, y int at -1/2

$\begin{gathered} y=\frac{A(x-1)^2}{(x+3)(x-2)^2} \\ -\frac{1}{2}=\frac{A(0-1)^2}{(0+3)(0-2)^2} \\ -\frac{1}{2}=\frac{A}{12} \\ 2A=-12 \\ A=-\frac{12}{2} \\ A=-6 \end{gathered}$

$y=\frac{-6(x-1)^2}{(x+3)(x-2)^2}$

Therefore the numerator is : -6(x-1)²

The denominator is : (x+3)(x-2)²