$[$k Nearest Neighbors$](10$ pts$)$

Consider properties of k$-$NN models:

a$.(2$ pts$)$ Suppose that we are using k$-$NN with just two training points, which have

different $($binary$)$ labels. Assuming we are using k $=1$ and Euclidean distance, what

is the decision boundary? Include a drawing with a brief explanation.

b$.(2$ pts$)$ For binary classification, given infinite data points, can k$-$NN with k $=1$ express

any decision boundary? If yes, describe the $($infinite$)$ dataset you would use to realize

a given classification decision boundary. If no$,$ give an example of a decision boundary

that cannot be achieved.

c$.(2$ pts$)$ Suppose we take k $$ ; what type of function does the resulting model family

become?