California Baptist University

(a) Suppose that $f$ is a function satisfying $|f(x)| \leq|x|$ for all $x$. Show that
$f \text { is continuous at } 0 . \text { (Notice that } f(0) \text { must equal } 0 .)$
(b) Give an example of such a function $f$ which is not continuous at any $a \neq 0$
(c) Suppose that $g$ is continuous at 0 and $g(0)=0,$ and $|f(x)| \leq|g(x)|$ Prove that $f$ is continuous at 0