1. **State the problem:** We are given the function $$y = \left(\frac{6}{x}\right)^2$$ and need to understand its behavior. 2. **Rewrite the function:** Using the property of exponents, we can write $$y = \frac{6^2}{x^2} = \frac{36}{x^2}$$. 3. **Important rules:** - The function is undefined at $$x=0$$ because division by zero is not allowed. - Since $$x^2$$ is always positive for $$x \neq 0$$, $$y$$ is always positive. 4. **Behavior:** - As $$x$$ approaches 0 from either side, $$y$$ approaches infinity. - As $$x$$ approaches infinity or negative infinity, $$y$$ approaches 0. 5. **Summary:** The function $$y = \frac{36}{x^2}$$ is a rational function with a vertical asymptote at $$x=0$$ and a horizontal asymptote at $$y=0$$. Final answer: $$y = \frac{36}{x^2}$$