Question

How do you find the domain and range of `f(x) =sqrt(x-2)`?

Answer 1

Domain `in [2,oo)`

Range `in [0,oo)`

Explanation:

graph{sqrt(x-2 [-10, 10, -5, 5]}

Simply draw out the function.

The standard root function is:

`y=a*sqrt((x-h)) +k`

where `x-h>=0`

In a square root function, the number inside the root sign CANNOT be `<0`

∴ `x-2>=0`

∴ `x>=2`

∴ Domain `in [2,oo)`

As for range, there is no K value in the function we were given
∴ the range begins at 0 to infinity.

Range `in [0,oo)`