Question

Explain how to graph -√(x-3). (How do you graph sqrt functions that have a negative sign in front of them?)

Answer 1

Firstly put $f(x) = \sqrt{x}$ then observe

$f(x+3)= \sqrt{x+3}$
$\Rightarrow -f(x+3) = -\sqrt{x+3}$

Then it becomes a case of standard transformations of the function f. i.e. take the regular square root function, shift it left 3 units and reflect it in the x-axis.