Question

How do you find the domain and range of `f(x)=sqrt(x-1)`?

Answer 1

domain is `x>=1`
range is `y>=0`

Explanation:

Domain

• can't be any number less than 1 ie `x!=0,-1,-2,...`
  So, domain is `x>=1`

Range

• based on the domain
• since domain starts at `x=1`, then the smallest y-value is `sqrt(1-1)=0`
  So, range is `y>=0`

Below is the graph, which you can see that domain is `x>=1` and range is `y>=0`
graph{sqrt(x-1) [-10, 10, -5, 5]}