1. **Problem statement:** Find the graph of the function $$g(x) = |x| + \frac{1}{\sin(4\pi)}$$. 2. **Analyze the function:** The function is composed of two parts: the absolute value function $$|x|$$ and the constant term $$\frac{1}{\sin(4\pi)}$$. 3. **Evaluate the constant term:** Since $$\sin(4\pi) = 0$$, the term $$\frac{1}{\sin(4\pi)}$$ is undefined (division by zero). 4. **Conclusion:** The function $$g(x) = |x| + \frac{1}{\sin(4\pi)}$$ is undefined for all $$x$$ because $$\sin(4\pi) = 0$$ makes the denominator zero, causing a division by zero error. Therefore, the function $$g(x)$$ does not exist as a real-valued function. **Final answer:** The function $$g(x)$$ is undefined for all real $$x$$ due to division by zero in the constant term.