1. **State the problem:** We need to analyze and draw the graph of the function $$f(x) = 3 - \sqrt{2 - x}$$. 2. **Understand the domain:** The expression under the square root must be non-negative: $$2 - x \geq 0$$ which simplifies to $$x \leq 2$$. So the domain is all real numbers $$x$$ such that $$x \leq 2$$. 3. **Analyze the function:** The square root function $$\sqrt{2 - x}$$ decreases as $$x$$ increases because the inside decreases. 4. **Calculate key points:** - At $$x = 2$$: $$f(2) = 3 - \sqrt{2 - 2} = 3 - 0 = 3$$ - At $$x = 1$$: $$f(1) = 3 - \sqrt{2 - 1} = 3 - 1 = 2$$ - At $$x = -2$$: $$f(-2) = 3 - \sqrt{2 - (-2)} = 3 - \sqrt{4} = 3 - 2 = 1$$ 5. **Behavior:** As $$x$$ decreases below 2, $$\sqrt{2 - x}$$ increases, so $$f(x)$$ decreases. 6. **Summary:** The graph starts at point $$(2,3)$$ and decreases as $$x$$ moves left, with domain $$(-\infty, 2]$$. Final answer: The function $$f(x) = 3 - \sqrt{2 - x}$$ is defined for $$x \leq 2$$ and decreases from $$3$$ downward as $$x$$ decreases.