Which is the asymptote of h (x) = 4 x -2?

No matter what real value you pick for  x ,  4^x > 0 ,

but  4^x  will approach  0  as  x  gets more and more negative.

 

So 4^x - 2  will approach  -2  as  x  gets more negative.

 

So the asymptote is at  y = -2 .