set terminal png
set output 'plot.png'
set xrange [0:pi]  # or you can use set xrange [0:*]
set yrange [-2:2]
set xlabel "x-values"
set ylabel "y-values"
set title "Function plots"
set samples 1000

# Define the functions
f1(x) = sin(sqrt(x))**2
f2(x) = exp(-x/2)*cos(2*pi*x)
f3(x) = 12.34*x**(5.0/3.0)

# Plot the functions with different line styles and widths
plot f1(x) title "f1(x)" lw 2 lc rgb "red", \
     f2(x) title "f2(x)" lw 3 lc rgb "blue", \
     f3(x) title "f3(x)" lw 4 lc rgb "green"