Graphing $f(x) = \sqrt{-x + 2}$ from the graph of $y=\sqrt{x}$.
Correct Method
First graph $f(x) = \sqrt{x}$.
then $f(x) = \sqrt{x+2}$ (shift left 2)
then $f(x) = \sqrt{-x+2}$ (Reflect over Y-axis)
This gives the correct graph.
Incorrect Method
First graph $f(x) = \sqrt{x}$
then $f(x) = \sqrt{-x}$ (Reflect over Y-axis)
then $f(x) = \sqrt{-x+2}$ (this +2 gives the WRONG graph, because it shifts to the left, where to get the correct graph, you'd need to shift to the right)
Can someone explain why $+2$ doesn't behave as expected when the $x$ has already been negated into $-x$ ?
Thanks!