Answer
The provided statement is false. The correct statement is that “A rational function can have both a vertical asymptote as well as a horizontal asymptote”.
Work Step by Step
In the rational function, say $F\left( x \right)=\frac{P\left( x \right)}{Q\left( x \right)}$ , the vertical asymptotes are dependent on the denominator terms. That is, for the vertical asymptote, we put $Q\left( x \right)=0$.
Whereas, the horizontal asymptotes depend on the degree of the numerator and denominator term. For having horizontal asymptotes, the degree of the numerator should be either equal to or less than that of the denominator.
Therefore, a rational function can have both vertical and horizontal asymptotes. And thereby, the given statement is false.
