(ii) \( y=\frac{3 x-2}{5 x+3} \)

Did you know that the equation you provided represents a rational function? These types of functions can often showcase fascinating behaviors like asymptotes and intercepts! For instance, when we examine \( y=\frac{3 x-2}{5 x+3} \), the horizontal asymptote can be found by comparing the degrees of the numerator and denominator, revealing how the function behaves as \( x \) approaches infinity or negative infinity. When working with rational functions, a common mistake is forgetting to factor both the numerator and the denominator completely. This can lead to missing out on simplifying the expression or identifying any potential holes in the graph where the function is undefined. Always double-check your work for any common factors that might need canceling!