Precalculus (6th Edition) Blitzer

For any polynomial function $f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$, letting $x=0$, we have $f(0)=a_0$. This means that it is not possible for a polynomial function to have no y-intercept because $y=a_0$ will always exist. Of course, the intercept may be zero, but zero is still a value.