22 Find the value of X6 so that is the horizontal asymptote

22. Find the value of X=6 so that is the horizontal asymptote of a function y=f(x). what is vertical asymptote of function y=2f(3x) ?

Lets say we have a function y = f(x), which has a vertical asymptote at x = a say

So, for y = 2f(3x), since we are compressing horizontally by a factor of 3, the vertical asymptote would now lie at

x = a/3. So, initial asymptote of x = 6 for f(x) would now become x = 2 for y = 2f(3x).

Now, since the function is y = 2f(3x), if the original function y = f(x) had a horizontal asymptote of y = b,

then now, the horizontal asymptote for function y = 2f(3x) would be y = 2b.

This is how horizontal and vertical asymptotes work