1. The problem is to analyze and understand the function $$y=2-\sqrt{2-x}$$ and describe its graph. 2. The function involves a square root, so the expression inside the root must be non-negative for real values: $$2-x \geq 0 \Rightarrow x \leq 2$$. 3. The square root function $$\sqrt{2-x}$$ decreases as $$x$$ increases from $$-\infty$$ to $$2$$. 4. The function $$y=2-\sqrt{2-x}$$ starts at $$x=-\infty$$ with $$y=2-\sqrt{\infty} = -\infty$$ and increases to $$y=2-0=2$$ at $$x=2$$. 5. The domain is $$(-\infty, 2]$$ and the range is $$(-\infty, 2]$$. 6. The graph is a decreasing curve starting from very low values and approaching $$y=2$$ as $$x$$ approaches 2 from the left. 7. The function intercepts the y-axis at $$x=0$$: $$y=2-\sqrt{2-0}=2-\sqrt{2} \approx 0.5858$$. 8. There is no maximum or minimum inside the domain except the endpoint at $$x=2$$ where $$y=2$$ is the maximum value. Final answer: The graph of $$y=2-\sqrt{2-x}$$ is defined for $$x \leq 2$$, is increasing and bounded above by 2, with a y-intercept at approximately 0.5858.