1. y=2e^-x -3
2. y=2sin(3x+pi) - 1
3. y= {sqrt(-x) -4 < x < 0
{sqrt(x) 0 < x < 4
domain is asking for allowable x-values and range asks for resulting y-values, but i'm not sure how to do it for these.
ok, here is the algebra thought process involved for your first function $\displaystyle y = 2e^{-x} - 3$ ...
what is the domain and range of the parent function $\displaystyle y = e^{x}$ ?
what transformation occurs to $\displaystyle y = e^x$ if the sign of x is changed? how does that transformation affect the domain and range?
how does the transformation of multiplying $\displaystyle e^{-x}$ by $\displaystyle 2$ affect the domain and range?
finally, how does the final transformation of subtracting $\displaystyle 3$ from $\displaystyle 2e^{-x}$ affect the domain and range?