Calculus 10th Edition

Let $f$ be a function. Suppose that there exists some vertical, say $x=c$, which intersect the graph of $f$ at two distinct points, say $y_1$ and $y_2$. This means that the function $f$ for the point x has two distinct value, that is, $f(c)=y_1$ and $f(c)=y_2$, $y_1 \neq y_2$. But this result contradicts the hypothesis that $f$ is a function.