What is the range of the function y=square root x+5

Answer:Range of the given function is [ 5 , ∞ )Step-by-step explanation:Given function is [tex]y\:=\:\sqrt{x}+5[/tex]We need to find Range of the given function.The Range of function is the set of all possible values of the dependent variable ( here, y )  , after substituting the value of domain.We know that square root can not have negative value. So, Domain of the given function is all non negative real number.That is Domain = { x : x ∈ R and x ≥ 0 } = [ 0 , ∞ )Now for range,put x = 0 in given function,[tex]y\:=\:\sqrt{0}+5=5[/tex]  ⇒ Minimum value of range is 5put x = ∞ in given function,[tex]y\:=\:\sqrt{\infinity}+5=\infinity+5=\infinity[/tex]  ⇒ Maximum value of range is ∞Thus, Range  = { y : y ∈ R and y ≥ 5 } = [ 5 , ∞ )Therefore, Range of the given function is [ 5 , ∞ )