Perpendicular Asymptotes

Algebra Level 3

f(x)=x26x+62x4f(x)=\dfrac{x^2-6x+6}{2x-4} g(x)=ax2+bx+cxdg(x)=\dfrac{ax^2+bx+c}{x-d}

You are given two functions ff and gg above, where a,b,c,a, b, c, and dd are unknown constants. Also, you are given the following information about the function gg:

  • It has the same vertical asymptote as ff.

  • Its diagonal asymptote is perpendicular to that of ff, and these two asymptotes intersect each other on the yy-axis.

  • The graphs of ff and gg have two intersection points. One of them is at x=2x = -2. (In other words, f(2)=g(2)f(-2) = g(-2).)

What is the value of the other xx-coordinate where ff and gg intersect?

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