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. You can also specify persist or nopersist when you set a new terminal.
set term qt persist size 700,500
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 not possible because the main program has exited. If you want to leave a plot window open and fully mouseable after creating the plot, for example when running gnuplot from a script file rather than interactively, see pause mouse close (p. ).