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

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?

• 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?
– Joe
Jun 2, 2021 at 21:47
• It is similar to what people call a Lorentzian (especially physicists) Jun 2, 2021 at 21:49
• $2=2x^0$ is a polynomial of degree $0$. Jun 2, 2021 at 21:49
• 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.
– user882145
Jun 2, 2021 at 22:09
• I made a mistake, there is only one asymptote, I was calling a vertex an asymptote. Jun 2, 2021 at 23:07