Exercise 1.7.19
To graph \(f(x)=-\sqrt{1-x}\) we first graph the elementary function \(y=\sqrt{x}\).
Next we reflect this graph about the \(y\)-axis by replacing \(x\) with \(-x\): \(\quad y=\sqrt{-x}\)
We then reflect that graph about the \(x\)-axis by replacing \(y\) with \(-y\): \(\quad -y=\sqrt{-x}\).
Finally, we shift that graph one unit to the right by replacing \(x\) with \((x-1)\): \(\quad -y=\sqrt{-(x-1)}\)
This is algebraically equivalent to \(y=-\sqrt{1-x}\).
