Posted by amy on Saturday, December 17, 2011 at 9:13pm.
determine the domain, range and horizontal asymptote Please show all your work
f(x) =  (3/4)^x  1
Help!

algebra  Reiny, Saturday, December 17, 2011 at 10:56pm
domain : any real value for x
range : y > 1
horizontal asymtote: y = 1
domain and range, just look at a sketch of the graph
last part:
intuitively, as x > ∞+ , value of (3/4)^x > 0
( e.g. (3/4)^100 = 3.2 x 10^13 , pretty close to zero)
as x  > ∞
we get (3/4)^x
= (4/3)^ +x > ∞
so look at x > +∞
f(x) > 0  1 = 1
so y = 1 is the horizontal asymtote