(a) In each part, either sketch an example of a function f with the given properties, or say that no such function exists. Make sure any sketches clearly meet the

given the conditions. \text { i. } f(1)=5 \text { and } \lim _{x \rightarrow 1} f(x)=3 .f is continuous on the domain (-0,0), and lim f(x) does not exist. \text { iii. } f \text { is continuous on the domain }(-\infty, \infty), \text { and } \lim _{x \rightarrow 3} \frac{f(x)-f(3)}{x-3} \text { does not exist. } ) Write a formula for a function f which satisfies the following conditions: \lim _{x \rightarrow 3} f(x)=-\infty \lim _{x \rightarrow-\infty} f(x)=4, \text { and } \lim _{x \rightarrow \infty} f(x)=4