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

Jul 13, 2015

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 $\left(x - 2\right)$-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 $\sqrt{x}$:
graph{sqrtx [-5.99, 22.48, -5.92, 8.32]}