Question

How do you graph `y=2-sqrt(x-2)`?

Answer 1

Take the graph of `y=sqrt(x)`, shift (translate) it to the right by 2 units, reflect it across the `x`-axis, then shift (translate) it up by 2 units.

Explanation:

Given a function `g(x)`, to get the graph of `y=g(x-2)` you should shift the graph of `y=g(x)` to the right by 2 units. Then to get the graph of `y=-g(x-2)` you should reflect the graph of `y=g(x-2)` across the `x`-axis. Finally, to get the graph of `y=2-g(x-2)` you should shift the graph of `y=-g(x-2)` up by 2 units.

You can also plot some points to help. Let `f(x)=2-sqrt{x-2}`. Then `f(2)=2-sqrt{0}=2`, `f(3)=2-sqrt{1}=1`, `f(4)=2-sqrt{2} approx 0.59`, `f(5)=2-sqrt{3} approx 0.27`, `f(6)=2-sqrt{4}=0`, `f(7)=2-sqrt{5} approx -0.24`, etc...

graph{2-sqrt(x-2) [-1, 10, -2.5, 2.5]}