set terminal png
set output 'plot.png'

set xrange [-2:3]
set yrange [-5:5]
set xtics 1
set ytics 2
set title "Piece-wise continuous functions"

f(x) = (x >= 2) ? (1.45 * x**3 - 6 * sqrt(x)) : 1/0
g(x) = (x >= -1 && x < 2) ? sin(x)**2 : 1/0
h(x) = (x < -1) ? abs(x) * exp(x) : 1/0

plot f(x) title "f(x) = 1.45x^3 - 6√x, x ≥ 2" lw 2 lc rgb "red", \
     g(x) title "g(x) = sin^2(x), -1 ≤ x < 2" lw 2 lc rgb "blue", \
     h(x) title "h(x) = |x| e^x, x < -1" lw 2 lc rgb "green"