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

May 17, 2018

domain is $x \ge 1$
range is $y \ge 0$

#### Explanation:

Domain

• can't be any number less than 1 ie $x \ne 0 , - 1 , - 2 , \ldots$
So, domain is $x \ge 1$

Range

• based on the domain
• since domain starts at $x = 1$, then the smallest y-value is $\sqrt{1 - 1} = 0$
So, range is $y \ge 0$

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