Why do rational functions like $\frac{1}{x}$ have weird shapes?

Question

As many know, rational functions have weird shapes like hyperbolas placed diagonally. They are in couple parts, for example $\frac{1}{x}$. Why does that happen?

Answer 1

I would rather consider the shape of this graph beautiful than weird. Rational funcions have shapes like this because of their nature where variable is in the denominator. When denominator approaches $0$ from both sides, the value rapidly increases or decreases into infinity. This is called an asymptote.