what are functions and how to justify them?

 Functions

what are functions and how to justify them?

A function f is a rule that assigns to each element x in a set D exactly one element, called f(x), in a set E

For example:


this is a function but be careful the same value in the domain can't take two values of co-domain



to make it easier to justify that the graph is a function is to make a vertical line test

The Vertical Line Test: A curve in the xy-plane is the graph of a function of x if and only if no vertical line intersects the curve more than once





one of the most important properties function can have is monotonic, what does that mean? 
it's when your function is increasing or decreasing



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