#y = (0.5)^x#

domain (the values that #x# could take):

#x# could be substituted for all real numbers, including #pi# and #e#.

this means that the values that #x# could take go from #-oo# to #oo#.

#therefore -oo# and #oo# are the domain, and are written as #(-oo,oo)#

range (the values that #y# could take):

#y = (0.5)^x#

the roots (square, cube, etc.) of negative numbers are lateral (#i# or a factor/multiple of this), and 0.5 is a real number-

#therefore (0.5)^x >0#.

since the value of #(0.5)^x# decreases as #x# increases, #y# gradually goes towards #0#.

although it does not actually reach #0#, #0# is its limit as #x# approaches #oo#.

this means that the values #y# could take go from #0# to #oo#.

#therefore 0# and #oo# are the range, and are written as #(0, oo)#.