documentclass[border=10pt]{standalone}
     usepackage{unicode-math}
     setmainfont{XITS}
     setmathfont{XITS Math}
     usepackage{pgfplots}
     usepackage{mathrsfs}
     pgfplotsset{compat=1.16}
     usetikzlibrary{intersections}
     usepgfplotslibrary{fillbetween}
     begin{document}
     begin{tikzpicture}
       [extended line/.style={shorten >=-#1,shorten <=-#1},
        /pgf/declare function={f(x)= exp(x);},
        /pgf/declare function={g(x)= x+1;}]
     begin{axis}[
       x=1.5cm,y=1.5cm,
       xtick={-4,...,4},ytick={-1,...,6},
       ymin=-2,ymax=7,xmin=-5,xmax=5,
       axis on top=false,
       enlargelimits=false,
       axis x line=middle,
       axis y line=middle,
       tick align=outside,
       tickwidth=0.12cm,
       xticklabels={empty,empty,empty,empty,0,1,empty,empty,empty},
       yticklabels={empty,0,1,empty,empty,empty,empty,empty},
       major tick style = {thick, black},
       axis line style = ultra thick,
       extra x ticks={-5,5},
       extra x tick label={null},
       extra y ticks={-2,7},
       extra y tick label={null},
       extra tick style={tick style={draw=none}},
       xlabel=,ylabel=,
       every axis x label/.style=
       {
       at={(ticklabel* cs:1)},
       anchor=west
       },
       every axis y label/.style=
       {
       at={(ticklabel* cs:1)},
       anchor=south
       },
       >=stealth,
       samples=2000,
       grid=none]

       addplot [thick,domain=-5:5] {g(x)};
       addplot [thick,domain=-5:5] {f(x)};

       draw[thick,->] (0,1) -- (1,1);
       draw[thick,->] (1,1) -- (1,2);

       node[below] at (0.5,1)  {$Delta x=1$};
       node[right] at (1,1.5)  {$Delta y=1$};

       node[right,black] at (1.5,{f(1.5)}) {$mathcal{C}_{x,longmapsto , {rm e}^x}$};

       node[below left] at (0,0) {0};

       end{axis}
       end{tikzpicture}
       end{document}