How do you find the vertical, horizontal and slant asymptotes of: #h(x) = log(x^2-4)/log(x/3)#?

1 Answer
Nov 30, 2016

Answer:

#x>2#. x = 2 (#uarr#) and x = 3 are the vertical asymptotes, y = 2 (#rarr#) is the horizontal asymptote. The x-intercept is #sqrt 5#.

Explanation:

h(x) is a bijective function for #x in (2, oo)#.

#x>2#. to make h real.

As #x to 2_=, y to -oo#.

As #x to oo, y to 2# ( from below ).

As #x to 3, y to +-oo#

x = 2 (#uarr#) is the vertical asymptote, y = 2 (#rarr#) is the

horizontal asymptote. The x-intercept is #sqrt 5#.

#y in (-oo, oo)#.

The left portion of the graph is for #x in (2, 3]#

graph{y-log(x^2-4)/log(x/3)=0 [-41.92, 41.93, -20.94, 21]}