gnuplot -persist -e 'plot [-5:5] sinh(x)'
gnuplot will open a display window, draw the plot into it, and then exit, leaving the display window containing the plot on the screen. Depending on the terminal type, some mousing operations may still be possible in the persistent window. However operations like zoom/unzoom that require redrawing the plot are generally not possible because the main program has already exited.
You can also specify persist or nopersist at the time you set a new terminal type. For example
set term qt persist size 700,500
Copyright 1986 - 1993, 1998, 2004 Thomas Williams, Colin Kelley
Distributed under the gnuplot license (rights to distribute modified versions are withheld).