How do you find the domain and range of #y = sqrt(9 + x)#?

1 Answer
Jul 27, 2016

Answer:

Domain: #[-9,oo)#
Range: #[0,oo)#

Explanation:

Assuming we are working strictly within the reals, the square root function requires nonnegative values. Thus the domain of the function #f(x) = sqrt(9+x)# is the set of values for #x# such that #9+x>=0#, that is, where #x>=-9#.

As #9+x# varies from #0# to #oo#, #sqrt(x+9)# varies from #0# to #oo#.

Thus, the domain of #sqrt(x+9)# is #[-9,oo)# and its range is #[0,oo)#