Horizontal asymptote?

Question

y=(2x)/(√(x^2-5x+6))

 

How do you get one side to be >-2 and the other >2

 

This is for Grade 12 Advanced Functions.

Answer 1

y = 2x/√(x²-5x+6)

 

y² = 4x²/(x²-5x+6)

 

Since the numerator and denominator are the same degree, y² has a horizontal asymptote equal to the ratio of the x² terms = 4x²/x² = 4.  Since y² has a vertical asymptote at y=4, y has vertical asymptotes at y = √y² = √4 = ±2  (x = 2 and x = -2).

 

BTW, the denominator factors to (x-2)(x-3), so y has vertical asymptotes at x = 2 and x = 3.  Click on the link below for the graph.

 

http://www.wyzant.com/resources/files/296832/graph_of_rational_function_showing_asymptotes