How do you find the domain and range for #y= (x+3)^0.5#?

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Answer 1 · 2018-05-29T17:06:55

Domain: #{x|x>=-3}# or #[-3, oo)#

Range: #{y|y>=0}# or #[0, oo)#

#y= (x+3)^0.5#

#y= (x+3)^(1/2)#

#y= sqrt(x+3)#

So the domain will be all numbers where the terms under the radical are not negative (otherwise the solution is imaginary).

#x+3>=0#

#x>=-3#

Domain: #{x|x>=-3}# or #[-3, oo)#

Now the range at #x=-3; y=0# but it will always be greater than or equal to 0.

Range: #{y|y>=0}# or #[0, oo)#

Here is the graph:

graph{sqrt(x+3) [-6, 14, -1.28, 8.72]}