Rational Functions

Definition

Rational functions are functions that can be expressed as a ratio (fraction) of two polynomials. They have both a numerator and denominator, where neither can be zero simultaneously.

Analogy

Imagine rational functions as recipes for smoothies. The numerator represents all the delicious ingredients, while the denominator acts like a blender that ensures everything is mixed well and doesn't explode.

Related terms

Polynomial Functions: Polynomial functions consist only of terms with non-negative integer exponents. They do not have any fractional or negative exponents.

Asymptotes: Asymptotes are lines that serve as boundaries for rational functions. They indicate where the graph approaches but never touches or crosses.

Vertical Asymptote: A vertical asymptote occurs when the denominator in a rational function becomes zero, causing an undefined value at that point.