What is the domain and range of # y = 3 sqrt(x-4) + 2#?

1 Answer
Jul 9, 2018

Answer:

Domain is # x >= 4 or x in [4,oo)#.
Range is # y >= 2 or y in [2,oo)#.

Explanation:

# y= 3 sqrt(x-4)+2 ; y# is undefined , if under root function is

#<0 :. x-4 >=0 :. x>= 4# . Domain is possible input of #x#

Domain is # x >= 4 or x in [4,oo)#.

Range is possible output of #y:. y>= 3*0+2 or y>= 2#

Range is # y >= 2 or y in [2,oo)#.

graph{3(x-4)^0.5+2 [-20, 20, -10, 10]}[Ans]