Question

How do you find the domain and range of `y=-2^(x)+3`?

Answer 1

Domain is `D=RR`, range is `(-oo;3)`

Answer:

The domain of an expresion is the largest subset of `RR` for which the expresion can be calculated. Possible limitations can be:
1) unknown in denominator of fractions (this cannot be zero)
2) expresions with unknown under square root sign (the square root of a negative number is not a real number)
3) expresions with unknown and logarythms. The expresion in logarythms can only be greater than 0.

In this example there are no such elements so the domain is not limited.

To calculate range you have to start from the range of exponential function `y=2^x`. This is `(0,oo)`
When you multiply such function by (-1) (the minus sign before `2^x`) the range turns to `(-oo,0)`.
Finally if you add 3 the range also moves, so finally you get `(-oo;3)`