posted by steve .
the domain and range of f(x)=(e^-x)-2
Start with the base function: y=e^x.
The range of y=e^x is (0, infinity).
If you have y=e^-x, that flips the function over the y axis, which does not change the range.
Now factor in the -2. That shifts the function down, so subtract 2 from the range: (-2, infinity)
Oops, forgot the domain.
e^x exists for all real values of x, so e^-x does also.
Therefore, the domain is (-infinity, infinity)