it's a plot of the exponential function and its 4th-order Taylor approximation, i.e. ${\displaystyle 1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+{\frac {x^{4}}{24}}}$. I have made it with Gnuplot, using the following code:

# set the output
set terminal svg enhanced fname "Times" fsize 18
set output "Taylorspolynomialexbig.svg"

# axis properties
set xrange [-4:4]
set yrange [-1:20]
set xzeroaxis linetype -1 linewidth 0.5
set yzeroaxis linetype -1 linewidth 0.5
set xlabel "x"
set key 0.15,19

plot exp(x) ti "exp(x)" with lines linewidth 3,\
     1+x+(x**2)/2+(x**3)/6++(x**4)/24 ti "4th-order Taylor" with lines linewidth 3