How do you find the domain and range for #y=sqrt(x+4)#?

1 Answer
Alan P.
Jan 4, 2016

Domain: #x>=(-4)# (could also be written as: #x in[-4,+oo)# )
Range: #y>=0# could also be written as: #y in [0,+oo)# )

Explanation:

To determine the domain we need to ask:
#color(white)("XXX")#For what values of #x# is #sqrt(x+4)# valid?

We know that #sqrt("something")# is valid if and only if #"something" >=0# (assuming we are restricted to Real numbers).

Therefore #(x+4)# must be #>=0#
#rArr x>=-4#

To determine the range we need to ask:
#color(white)("XXX")#What values can be generated using legal values of #x# by the expression #sqrt(x+4)#

When #x=-4#
#color(white)("XXX")sqrt(x+4)=0#
When #x> -4#
#color(white)("XXX")sqrt(x+4)>0# with no upper limit as #xrarr+oo#

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