Answer
The graph can have one horizontal asymptote at most.
Work Step by Step
When calculating $\displaystyle \lim_{x\rightarrow\pm\infty}\frac{f(x)}{g(x)}$, then we know that the limit exists if
(the degree of g) $\geq$ (the degree of f),
in which case we will divide the numerator and denominator with $x^n$, the highest power of x in the expression.
If g has a greater degree than f, the limit is zero, whether $ x\rightarrow\infty$ or $ x\rightarrow-\infty$
If the degrees are equal, the limit is the quotient of leading coefficients, whether $ x\rightarrow\infty$ or $ x\rightarrow-\infty$
In either case, only one limit is possible, so the graph can have one horizontal asymptote.
