Question

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

Answer 1

Domain: `x>= 2` Range: `y>=0`

Explanation:

Basically, the domain is the values of x that keep your function or equation defined. You cannot have a negative value in the square root.

• So the domain is
  `x-2>=0`
  `x>=2`

• Because `sqrt(2-2) =0 , sqrt(3-2)=1` etc any smaller x leaves us with a complex number and we don't want that.

It also helps to draw the function to see. For y, it is easy to see if you draw the function that the smallest y possible is 0 before the curve goes to infinity.

• Hence why our range is:
  `y>=0`
  Hope this helped, any corrections welcome :)

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