1. **State the problem:** Identify the graph of the equation $$y - 3 = \sqrt{x - 2}$$. 2. **Rewrite the equation:** Add 3 to both sides to isolate $$y$$: $$y = 3 + \sqrt{x - 2}$$ 3. **Domain and range:** - The expression under the square root must be non-negative, so $$x - 2 \geq 0 \Rightarrow x \geq 2$$. - The square root function outputs values $$\geq 0$$, so $$y \geq 3$$. 4. **Graph characteristics:** - The graph starts at the point where $$x=2$$, $$y=3$$. - It moves rightward (increasing $$x$$) and curves upward because the square root function increases but at a decreasing rate. 5. **Match with given graphs:** - Left graph: x-axis from -6 to 2, y-axis from -8 to 2, curve starts near (2,3) but y-axis max is 2, so it cannot show $$y=3$$. - Center graph: x-axis from -8 to 6, y-axis from -8 to 2, y max is 2, so cannot show $$y=3$$. - Right graph: x-axis from -2 to 6, y-axis from -2 to 8, curve starts near (2,3) and moves upward to the right, matching the equation. **Final answer:** The right graph corresponds to the equation $$y - 3 = \sqrt{x - 2}$$.