Question

How do you graph `y=sqrtx-2` and what is the domain and range?

Answer 1

See below.

Explanation:

The graph looks like this:

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

The domain is all possible values of `x` that give out a defined value of `f(x)`.

Here, `y` will be undefined if `x<0`, as the square root function cannot, really, have an input below `0`

So `x>=0`.

In interval notation, the domain is `[0,oo)`.

The range is all possible outputs of `f(x)`.

Since a square root function does not give an answer above `0`, the range of `sqrt(x)` is `y>=0`. However, since the above function is `sqrt(x)-2`, the range is `y>=-2`, or in interval notation:

`[-2,oo)`.