Question

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

Answer 1

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]