y= 3(2^{x-1})-4

is there a way to find them without graphing, simply?

The range is all real numbers.

2 to the power of any number must be greater than 0

3* a number that is greater than 0 is greater than 0

-4 and the outcome must be greater than -4

Hence the range will be y>-4 with and asymtote at y=-4

CHECK