1. **State the problem:** Identify the graph of the equation $$y - 3 = \sqrt[3]{x - 4}$$. 2. **Rewrite the equation:** The equation can be written as $$y = 3 + \sqrt[3]{x - 4}$$. 3. **Understand the cube root function:** The cube root function $$\sqrt[3]{x}$$ is an odd function with a characteristic S-shaped curve passing through the origin. 4. **Transformation:** The graph of $$y = \sqrt[3]{x}$$ is shifted right by 4 units (due to $$x - 4$$) and up by 3 units (due to the +3). 5. **Graph behavior:** - At $$x=4$$, $$y=3+\sqrt[3]{0}=3$$. - For $$x > 4$$, $$y$$ increases slowly. - For $$x < 4$$, $$y$$ decreases slowly. 6. **Match with given graphs:** - The graph should have a bend near $$x=4$$ and pass through $$y=3$$ at $$x=4$$. - The center graph shows a curve starting near $$y=0$$ at $$x=0$$ and rising smoothly with a bend near $$x=4$$. - The bottom-left graph has a curve starting below $$y=-4$$ near $$x=0$$, which does not match the vertical shift. - The bottom-right graph is shifted left and does not match the horizontal shift. **Conclusion:** The center graph corresponds to the equation $$y - 3 = \sqrt[3]{x - 4}$$.