For which value of x does the function \(f(x) = \frac{2x-6}{x^3 - 7x^2 - 2x + 6}\) cross its horizontal asymptote?
+128460 We have a "low/ high" situation....so.....this graph has a horizontal asymptote at y = 0
So....we need to solve this
2x - 6
______________ = 0
x^3 -7x^2 -2x + 6
Only an x value in the numerator can make this = 0
So
2x - 6 = 0 add 6 to both sides
2x = 6 divide both sides by 2
x = 3
So....it crosses its horizontal asymptote at (3, 0)
See the graph here :
https://www.desmos.com/calculator/fotxpapass
