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

Jun 1, 2018

Dom f(X): $\mathbb{R}$
Ran f(X): $\left(- \infty , 2\right)$

#### Explanation:

The domain of a exponential function is Usually $\mathbb{R}$
Unless, the domain is restricted this usually specified by the use of function notation in the question.

The range of the most basic exponential $f \left(X\right)$ is:
${\mathbb{R}}^{+}$ 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.