Let $f\colon E\to \mathbb{R}$ be continuous at $p \in E$. Prove that there exists a positive constant $M$ and $\delta > 0$ such that $|f(x)| \le M$ for all $x \in E \cap N_\delta(p)$.
The book says to take $\epsilon = 1$, then there exists a $\delta > 0$ such that $|f(x) - f(p)| \le 1$, for all $x \in E \cap N_\delta(p)$.
How would I start this?