[Q32 60 points] Consider the following types of functions. I Increasing function I Lines: function I Homogeneous function I Concave function I Quasiconcave function I Continuous function (a) Write down the \"formal" denition of each type of function using mathematical symbols and as few english words as possible. Highlight the l\"minimal structure\" required on the input set and the output set to dene each type of function. (h) Then, express the denition in words using as few mathematical symbols as possible. (c) Construct an example of each type of function mentioned above. Please use a f : R2 } R. Draw the 313 version gure and its 2D oontour plot. Use any software you wish. (d) Construct a counterexample for each type of function mentioned above. Prove that the coun- terexample is indeed a counterexample. You can answer (a) and (b) in one table. For [(1), try to nd the simplest counterexample which helps you better understand the denition