The Domain is the list of all x values that are allowable in the function.
When answer Domain questions, I like to look at what happens when I set x=0, oo, -oo and any other value that might cause the function to not operate.
When x=0, y=2^0=1 and so no problem there
When x=oo, y=2^(oo)=oo and so no problem there
When x=-oo, y=2^(-oo)=1/(2^(oo))=0 and so no problem there
In fact, there are no x values that are disallowed, and so we can say that all real numbers are in the list of allowable values. We can write that in math terms as:
x in RR
The Range is the list of all resulting Domain values (and is usually the list of y values). We've already seen that y can be 0, can be 1, can be infinitely big. We can't make y be less than 0 - there is no x value we can plug in that will make y negative. We can write that as:
y>=0
We can see this is the graph of y=2^x:
graph{2^x [-5,10,-5,20]}
