GNUplot example for https://stackoverflow.com/a/52210067/116639

file.dat

1 0.000000
2 0.301030
3 0.477121
4 0.602060
5 0.698970
6 0.778151
7 0.845098
8 0.903090
9 0.954243
10 1.000000

plot.1.gp

# function extends to infinity, initial zoom is 1:10
plot "file.dat" using 1:2 with lines, sin(x)

plot.2.gp

# function is limited to range, initial zoom is 1:10
plot "file.dat" using 1:2 with lines, [1:3] sin(x)

plot.3.gp

# function extends to infinity, initial zoom is 1:3
plot [1:3] sin(x), "file.dat" using 1:2 with lines

plot.4.gp

# function extends to infinity, initial zoom is 1:3
plot [1:3] sin(x), [1:10] "file.dat" using 1:2 with lines