1. The problem is to analyze and graph the function $$y = X^{\frac{2}{3}} + \sqrt{3.3 - X^{2}} \cdot \sin(6.41 \cdot 3.14 \cdot X)$$. 2. This function combines a power term, a square root term, and a sinusoidal term. The domain is restricted by the square root: $$3.3 - X^{2} \geq 0 \Rightarrow |X| \leq \sqrt{3.3}$$. 3. The function is defined for $$X \in [-\sqrt{3.3}, \sqrt{3.3}]$$. 4. The first term $$X^{\frac{2}{3}}$$ is the cube root squared, which is defined for all real $$X$$ and is always non-negative. 5. The second term $$\sqrt{3.3 - X^{2}} \cdot \sin(6.41 \cdot 3.14 \cdot X)$$ oscillates between positive and negative values because of the sine factor, but the amplitude is modulated by the square root term. 6. To graph this function, plot $$y$$ versus $$X$$ over the domain $$[-\sqrt{3.3}, \sqrt{3.3}]$$. 7. The function has intercepts where $$y=0$$, and extrema where the derivative equals zero, which can be explored graphically. Final answer: The function is $$y = X^{\frac{2}{3}} + \sqrt{3.3 - X^{2}} \cdot \sin(6.41 \cdot 3.14 \cdot X)$$ with domain $$X \in [-\sqrt{3.3}, \sqrt{3.3}]$$.