Follow the seven step strategy to graph the following rational function. \[ f(x)=\frac{x^{2}+x-12}{x^{2}-4} \] A. The equation(s) of the horizontal asymptote(s) is/are \( y=1 \). (Type an equation. Use a comma to separate answers as needed.) B. There is no horizontal asymptote. Plot points between and beyond each \( x \)-intercept and vertical asymptote. Find the value of the function at the given value of \( x \). \[ \begin{array}{lllllll} x & -11 & -9 & -1 & 1 & 6 & 11 \\ f(x)=\frac{x^{2}+x-12}{x^{2}-4} & \square & \square & \square & \square & \square & \square \end{array} \] (Simplify your answers.) Use the information obtained in the previous steps to graph the function between and beyond the vertical asymptotes. Choose the correct graph below. A. B. C. D. \( 2 n \) Ay \( -2 n x^{4} \) \( - \) \( 4{ }^{4 y} \) \( -2 n^{4 y} \) \( { }^{*} \) \( \sqrt{11} \) \( \sqrt[11]{11} \) \( \pi \) \( \infty \) More Next
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The vertical asymptotes occur where the denominator is zero. Solve \(x^2 - 4 = 0\). \[ x^2 - 4 = (x-2)(x+2) = 0 \] So, \(x = 2\) and \(x = -2\) are vertical asymptotes. Show more…
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