a) \( F(x)=\frac{x}{2-x} \)

Did you know that functions like \( F(x)=\frac{x}{2-x} \) reveal fascinating behaviors when graphed? For instance, if you plot this function, you'll see an interesting vertical asymptote at \( x=2 \), where the function heads to infinity. It's essentially a visual way of seeing how the function behaves as it approaches certain points—just like a roller coaster that takes a steep dive! Now, let’s talk about a real-world application! This type of function can model situations such as profit margin ratios or population growth under constraints. When there’s a limit to resources, those functions can help predict changes in outcomes, guiding businesses or ecologists in making informed decisions. It’s like being a financial wizard or a nature detective at the same time!