Is there a term for this type of equation? $$y = \frac{2}{x^2+16}$$

It has two vertical asymptotes. If the degree of the variable in the denominator is higher than the degree of the variable in the numerator there is one horizontal asymptote at $0$. So I gather the number $2$ does not count as having a degree hence this is not a rational expression. Is there a name for it?

  • 5
    $\begingroup$ Any function which can be written as $$\frac{\text{polynomial}}{\text{another polynomial}}$$ is called a rational function. NB the number $2$ is a polynomial. Does that help? $\endgroup$
    – Joe
    Jun 2, 2021 at 21:47
  • $\begingroup$ It is similar to what people call a Lorentzian (especially physicists) $\endgroup$
    – Evariste
    Jun 2, 2021 at 21:49
  • 2
    $\begingroup$ $2=2x^0$ is a polynomial of degree $0$. $\endgroup$
    – Stuck
    Jun 2, 2021 at 21:49
  • 3
    $\begingroup$ How are there two vertical asymptotes when the denominator is never equal to zero? Is your expression typed correctly? $ \ \frac{2}{x^2 - 16} \ $ has two vertical asymptotes. $\endgroup$
    – user882145
    Jun 2, 2021 at 22:09
  • $\begingroup$ I made a mistake, there is only one asymptote, I was calling a vertex an asymptote. $\endgroup$
    – Rolomoto
    Jun 2, 2021 at 23:07


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