1. The problem asks for the domain of the function $r(x) = \sqrt{1 - x}$.\n\n2. The domain of a square root function includes all $x$ values for which the expression inside the square root is non-negative because the square root of a negative number is not a real number.\n\n3. Set the expression inside the square root greater than or equal to zero:\n$$1 - x \geq 0$$\n\n4. Solve the inequality for $x$:\n$$1 - x \geq 0$$\n$$\Rightarrow -x \geq -1$$\n$$\Rightarrow \cancel{-x} \leq \cancel{-1} \quad \text{(dividing both sides by -1 reverses inequality)}$$\n$$x \leq 1$$\n\n5. Therefore, the domain is all real numbers $x$ such that $x \leq 1$.\n\n6. In interval notation, the domain is $$(-\infty, 1]$$\n\nThis means $r(x)$ is defined for all $x$ values less than or equal to 1.