I have difficulty understanding the concept of "Function" and "Limit of a Function", Please help.

A function is a process with an input and an output, for any given input a function will only have one output.

You may for instance have a function [math]f:x\to x+1[/math] where for any imput x, the output will be x+1

 

The limit of a function is what the output tends to (gets closer and closer to but might not ever actually get there) as the input gets more extreme. In the example I gave above, as x gets higher so does f(x), so: [math]\lim_{x \to \infty}f(x)= \infty[/math] (this is pronounced: the limit, as x tends towards infinity, of f(x) is infinity)