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

##### 1 Answer
Jul 30, 2015

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 $g \left(x\right)$, to get the graph of $y = g \left(x - 2\right)$ you should shift the graph of $y = g \left(x\right)$ to the right by 2 units. Then to get the graph of $y = - g \left(x - 2\right)$ you should reflect the graph of $y = g \left(x - 2\right)$ across the $x$-axis. Finally, to get the graph of $y = 2 - g \left(x - 2\right)$ you should shift the graph of $y = - g \left(x - 2\right)$ up by 2 units.

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

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