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No. A relation is not a special type of function.
Create a scatter plot. That might give some indication of the function type. Try out different function. Once you get experience it will come easier.
In Excel, you can use the max() function. You can type a range (or several ranges) within the max() function. For a single range, just type: =max( and select the desired range, then type the closing parenthesis.
It is a linear function. That is to say, it is a function representing a straight line in the coordinate plane.
Assuming that b > 0, it is an inverse power function or an inverse exponential function.