Handbook of mathematics for engineers and scienteists part 3

This function is defined for all x, and its range coincides with the j/-axis. The arcsinh x is an odd. nonperiodic. unbounded function that crosses the axes Ox and Oy at the origin x = 0, y = 0. This is an increasing function on the entire real axis with no points of extremum. The graph of the function y = arcsinh x is given in Fig. 2.18.