Question

Consider the functions f(x) = (4/5)^x and g(x) = (4/5)^x  + 6. What are the ranges of the two functions?

Answer 1

THE RANGES OF THE TWO FUNCTIONS ARE
Y>0
Y>6

Answer 2

The range of the function is the set of all possible values that function can take. Both given functions

$y=\left(\dfrac{4}{5}\right)^x$ and $y=\left(\dfrac{4}{5}\right)^x+6$

are exponential functions with base $\dfrac{4}{5}.$

The graphs of these function you can see in attached diagram.

The range of the function $y=\left(\dfrac{4}{5}\right)^x$ is $(0,\infty).$

The range of the function $y=\left(\dfrac{4}{5}\right)^x+6$ (this function is translated function  $y=\left(\dfrac{4}{5}\right)^x$ 6 units up) is $(6,\infty).$