Question

How do you graph `y=3sqrt(x-2)`, compare it to the parent graph and what is the domain and range?

Answer 1

Explanation below
graph{3sqrt(x-2) [-6.63, 11.15, -2.41, 6.48]}
graph{sqrt(x) [-2.25, 10.235, -1.62, 4.624]}

Explanation:

The domain:
square root must be greater than 0 or equal
`x-2>=0`
`x>=2`
`x in <2,oo)`

As we can see the sqrt graph starts at x=2(it's shifted to the right). The number 3 in front says that it is going to be bigger than the parent graph(will be going up way more than default `sqrt(x)`)

Range: `f(x) in <0,oo)`