How would you find the domain and range of x=2^y?

Answer 1

When y = 0 then x = 1.

As y rises towards positive infinity, x rises towards positive infinity.

As y falls towards negative infinity, x falls towards 0.

There is no real value of y corresponding to any negative value of x.

-∞ ≤ y ≤ +∞
0 ≤ x ≤ +∞

Answer 2

your domain should have been

0 < x ≤ ∞

x can never become zero