all rational functions have at least one vertical asymptote. true false

Answer:

B. False

Explanation:

Step1: Recall rational - function definition

A rational function is of the form $f(x)=\frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials and $q(x)\neq0$.

Step2: Consider the case of no vertical asymptote

If $q(x)$ has no real - valued roots, then the rational function has no vertical asymptotes. For example, consider the rational function $f(x)=\frac{1}{x^{2}+1}$. The denominator $x^{2}+1$ has no real roots since $x^{2}+1 = 0$ gives $x^{2}=-1$, and $x=\pm i$ (complex numbers). So, not all rational functions have a vertical asymptote.