## Precalculus (6th Edition) Blitzer

If there is a rational function $f\left( x \right)=\frac{p\left( x \right)}{q\left( x \right)}$ where $p\left( x \right)$ is the numerator and $q\left( x \right)$ is the denominator then $x=a$ is a vertical asymptote of the function $f\left( x \right)$ if $x=a$ is a zero of the denominator $q\left( x \right)$. There is no value of $x$ for which the denominator is equal to zero. So, there is no vertical asymptote. If there is a rational function $f\left( x \right)=\frac{p\left( x \right)}{q\left( x \right)}$ where $p\left( x \right)$ is the numerator and $q\left( x \right)$ is the denominator then $x=a$ is called a hole if $x-a$ is a common factor of the numerator and denominator. So, there is no common factor between $x$ and ${{x}^{2}}+4$. Thus, there are no holes. Hence, there is no vertical asymptote and there are no holes.