Part 1/5:

Understanding Rational and Algebraic Functions

Mathematics can sometimes seem daunting, especially when it comes to functions. In this article, we delve into rational and algebraic functions, breaking them down into easily digestible segments.

What are Rational Functions?

A rational function is defined as a function ( f(x) = \frac{P(x)}{Q(x)} ), where ( P(x) ) and ( Q(x) ) are both polynomials. This implies that rational functions can be expressed as the ratio of two polynomial expressions.

The domain of a rational function refers to all possible values of ( x ) except those that would make ( Q(x) = 0 ). This restriction leads to points where the function is undefined. For instance, the function

[

f(x) = \frac{1}{x}

]