Question

How do you use the graph of `y=sqrtx` to sketch the graph of `f(x)= 3-sqrt(x-2)`?

Answer 1

We have to make a difference between the `3` and the `-2` under the root. Also look at the `-`sign in front of the root.

Explanation:

(1)
The `(x-2)`-part. This means that the curve is moved `2` to the right, because now it's zero when `x=2`
(2)
The `-`sign means everything is upside down.
(3)
The `3` means everything is moved up by `3`

Since there is nothing in front of the root-sign, the form stays the same. It's only moved `2` to the right, `3` up, and turned upside down.
graph{3-sqrt(x-2) [-5.99, 22.48, -5.92, 8.32]}
As compared to `sqrtx`:
graph{sqrtx [-5.99, 22.48, -5.92, 8.32]}