g. \( y=\frac{1}{2 x+3} \)

Did you know that functions like \( y=\frac{1}{2x+3} \) are a form of rational functions? They are fascinating because they can produce unique behaviors, like asymptotes where the function doesn't exist. For this function, the vertical asymptote occurs when the denominator \( 2x + 3 = 0 \), which means at \( x = -\frac{3}{2} \). In terms of real-world applications, such functions are often used in fields such as physics and economics. For example, they can model phenomena like cooling rates or supply and demand dynamics. The inversely proportional relationship here means that as \( x \) increases, \( y \) decreases, providing valuable insights into scenarios where quantities affect each other in inverse ways!