Can a Function Have Two Horizontal Asymptotes?

A function can have at most two different horizontal asymptotes. A graph can approach a horizontal asymptote in many different ways; see Figure 8 in §1.6 of the text for graphical illustrations.

What functions have 2 horizontal asymptotes?

Multiple Horizontal Asymptotes

Ok, so what kinds of functions have two horizontal asymptotes? One important example is the arctangent function, f(x) = arctan x (also known as the inverse tangent function, f(x) = tan^-1 x). As x→ ∞ the y-values approach π/2, and as x→ -∞, values approach -π/2.

Can an equation have more than one horizontal asymptote?

Asymptotes. A rational function can have at most one horizontal or oblique asymptote, and many possible vertical asymptotes; these can be calculated.