How do you find the domain and range for #(2/3)^x – 9#?

1 Answer
Jun 14, 2015

Answer:

#f(x) = (2/3)^x - 9#

#f(x)# is well defined for all #x in RR# so the domain is #RR#

By looking at end behaviour we find the range of #f(x)# is #(-9, oo)#

Explanation:

As #x->-oo# we have #(2/3)^x = (3/2)^(-x) -> oo#,

so #f(x) -> oo#

As #x->oo# we have #(2/3)^x->0#, so #f(x) -> -9#

So range #f(x) = (-9, oo)#

graph{(2/3)^x - 9 [-22.5, 22.5, -11.25, 11.25]}