1. The problem involves understanding the function $$f(x) = \sqrt{x} + \sin(x)$$ and the graph labeled as cm(x) with a length scale of 2 cm. 2. We start by analyzing each component: $$\sqrt{x}$$ is the square root function, defined for $$x \geq 0$$, and $$\sin(x)$$ is the sine function, which oscillates between -1 and 1. 3. The combined function $$f(x) = \sqrt{x} + \sin(x)$$ will have the domain $$x \geq 0$$ because of the square root. 4. The graph labeled cm(x) likely represents a scaled version of the function or a related measurement, with 2 cm indicating a length scale on the graph. 5. To understand the shape, note that $$\sin(x)$$ oscillates, so $$f(x)$$ will oscillate around the increasing curve $$\sqrt{x}$$. 6. The function $$f(x)$$ does not have a simple closed form for roots or extrema, but we can find critical points by differentiating: $$f'(x) = \frac{1}{2\sqrt{x}} + \cos(x)$$ 7. Setting $$f'(x) = 0$$ to find extrema: $$\frac{1}{2\sqrt{x}} + \cos(x) = 0$$ This equation can be solved numerically for $$x > 0$$. 8. The graph's scale of 2 cm likely helps measure distances or amplitudes on the graph but does not change the function's mathematical properties. Final answer: The function $$f(x) = \sqrt{x} + \sin(x)$$ combines a square root growth with sinusoidal oscillations, defined for $$x \geq 0$$, and the graph with scale 2 cm helps visualize this behavior.