Question

How do you find the domain and range of exponential functions `f(x) = 2 - e ^ (x / 2)`?

Answer 1

Dom f(X): `RR`
Ran f(X): `(-oo,2)`

Explanation:

The domain of a exponential function is Usually `RR`
Unless, the domain is restricted this usually specified by the use of function notation in the question.

The range of the most basic exponential `f(X)` is:
`RR^+` The range of a exponential can be altered by a vertical translation or by a reflection in the X axis or y-axis(depends),
Or a combination of these transformations.

For Working out range I think it is best you sketch the curve yourself or use a graphing app e.g Desmos or A Graphing calculator Like the CAS T-nspire.