Help me figure this out please? g(x) = e ^ x-7?

first, you need to understand the property of an exponential function.
e ^ x when x approach to infinity, e ^ x goes to infinity
e ^ x when x approach to negative infinity, e ^ x goes to 0
e ^ x = 1 when x = 0

Domain = interval for x that can make the function finite
Range = outcome of the function based on domain

In this case, domain = ( - inf , inf )
range = (0, inf)
I use ( ) instead of [ ] because the function can approach to infinity, but never reaches infinity.

horizontal asymptote = 0 because y never reaches 0, it can approach to 0.