As x approaches infinity, this function of x approaches e-to-the-x-power ov
As x approaches infinity, this function of x approaches e-to-the-x-power over two.  It ranges up to infinity but never takes a value lower than one.  It describes the shape of a hanging cable-the caternary-and it repeats itself every 2-pi-i radians in complex space.  FTP, name this hyperbolic function, defined as one-half times (e to the x) plus (e to the minus x).
As x approaches infinity, this function of x approaches e-to-the-x-power over two.  
hyperbolic cosine or cosh