You have the following function:
f(x) = 2(1/5)ˣ
in order to determine the end behavior of f(x), make x = ∞, and use exponential properties:
f(x) = 2(1/5)^∞
= 2(1^∞)/(5^∞)
= 2(1)/∞
= 0
next, for x = -∞
f(x) = 2(1/5)^(-∞)
= 2(1^-∞)/(5^-∞)
= 2(5^∞)/(1^∞)
= 2(∞)/1 = ∞
HENCE:
As x approaches infinity, f(x) approaches 0, as x approaches to negative infinity, f(x) approaches to infinity