Question

find the horizontal aysmtope

g(x)=9x^2-2x-5/2x^2-7x+2

Answer 1

find the limit as x approaches infinity

Answer 2

how?

Answer 3

divide both the numerator and the denominator by the term with the biggest degree, which is x^2
so you get
g(x)=(9-(2/x)-(5/x^2))/(2-(7/x)+(2/x^2))
the limit of all the other terms containing x are 0. and so the limit of the function is g(x)=(9x^2-2x-5)/(2x^2-7x+2)=9/2