Atualização 2 a pedido do OP

Question

Quero desenhar uma figura (no verso) conforme mostrado abaixo: um eixo numérico com alguns intervalos indicados por um número circulado:

Answer 1

Atualização 2 a pedido do OP

Criei um novo estilo chamado from inftypara representar o intervalo de -infinity. Para colocar o texto sob as figuras, nomeei a caixa delimitadora como machado e coloquei um nó abaixo dela.

from infty/.style args={#1of#2}{%<-- new style "from infty"
            to path={($(\tikztostart)!#1!90:(\tikztotarget)$).. controls ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
                .. (\tikztotarget) \tikztonodes}}

\documentclass[tikz,border=5mm]{standalone}
%\usepackage{tikz}
\usetikzlibrary{arrows.meta,calc,quotes}
\begin{document}

\tikzset{my curve/.style args={#1of#2}{
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            and ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget)\tikztonodes}},
             my curve/.default={7mm of 0.25},
             to infty/.style args={#1of#2}{%<-- new style "to infty"
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. ($(\tikztotarget)!#1!90:(\tikztotarget)$) \tikztonodes}},
            from infty/.style args={#1of#2}{%<-- new style "from infty"
        to path={($(\tikztostart)!#1!90:(\tikztotarget)$).. controls ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget) \tikztonodes}},
             to infty/.default={7mm of 0.4},
             from infty/.default={7mm of 0.4}}  

\begin{tikzpicture} [pics/tick/.style={code={\draw ++(0,-.2)node[below]{#1}--++(0,.4);}}]
\begin{scope}[local bounding box=axe]%<-- bounding box "axe"
\coordinate (z') at (-2,0);
\coordinate (c) at (1,0);
\coordinate (b) at (4,0);
\coordinate (a) at (6,0);
\coordinate (z) at (9,0);
\draw[-{Stealth[]}] (-2,0)--(10,0);
\pic at (c){tick=c};
\pic at (b){tick=b};
\pic at (a) {tick=a};
%\pic at (z) {tick};
\draw (z')to["4"{draw,circle},from infty](c) to["2"{draw,circle},my curve] (b) to ["3"{draw,circle},my curve] (a) to ["1"{draw,circle},to infty](z);
\end{scope}
\node[below] at (axe.south){My axis};%<-- node to add caption
\end{tikzpicture}

\end{document}

Atualização a pedido do OP

Criei um novo estilo chamado to inftypara representar o intervalo até o infinito. Para colocar texto sob as figuras, nomeei a caixa delimitadora axee coloquei um nó abaixo dela.

O código é comentado com %<--.

\documentclass[tikz,border=5mm]{standalone}
%\usepackage{tikz}
\usetikzlibrary{arrows.meta,calc,quotes}
\begin{document}

\tikzset{my curve/.style args={#1of#2}{
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            and ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget)\tikztonodes}},
             my curve/.default={7mm of 0.25},
             to infty/.style args={#1of#2}{%<-- new style "to infty"
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. ($(\tikztotarget)!#1!90:(\tikztotarget)$) \tikztonodes}},
             to infty/.default={7mm of 0.4}}  

\begin{tikzpicture} [pics/tick/.style={code={\draw ++(0,-.2)node[below]{#1}--++(0,.4);}}]
\begin{scope}[local bounding box=axe]%<-- bounding box "axe"
\coordinate (c) at (1,0);
\coordinate (b) at (4,0);
\coordinate (a) at (6,0);
\coordinate (z) at (9,0);
\draw[-{Stealth[]}] (0,0)--(10,0);
\pic at (c){tick=c};
\pic at (b){tick=b};
\pic at (a) {tick=a};
%\pic at (z) {tick};
\draw (c) to["2"{draw,circle},my curve] (b) to ["3"{draw,circle},my curve] (a) to ["1"{draw,circle},to infty](z);
\end{scope}
\node[below] at (axe.south){My axis};%<-- node to add caption
\end{tikzpicture}

\end{document}

Parâmetros de curva

Esses dois estilos são definidos, por padrão, aparece na figura anterior. É possível modificar oalturada curva e suacurvaturacom os seguintes parâmetros. Por exemplo my curve=12mm of .4significa que a curva tem umalturade 12 mme que oPontos de controleda curva de Bézier estão localizados 0.4no 1-0.4=0.6caminho.

\draw (c) to["2"{draw,circle},my curve=12mm of .4] (b) to ["3"{draw,circle},my curve=8mm of .2] (a) to ["1"{draw,circle},to infty=15mm of .6](z);

Primeira resposta

Eu reutilizei ominha curva 7código que escrevi aqui. Eu renomeei isso my curve.

\tikzset{my curve/.style args={#1of#2}{
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            and ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget)\tikztonodes}},
             my curve/.default={7mm of 0.25}} 

Eu defini um picque permite desenhar uma marca e escrever um texto abaixo.

pics/tick/.style={code={\draw ++(0,-.2)node[below]{#1}--++(0,.4);}}

Resultado:

Código:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,calc,quotes}
\begin{document}

\tikzset{my curve/.style args={#1of#2}{
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            and ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget)\tikztonodes}},
             my curve/.default={7mm of 0.25}}  

\begin{tikzpicture} [pics/tick/.style={code={\draw ++(0,-.2)node[below]{#1}--++(0,.4);}}]

\coordinate (c) at (1,0);
\coordinate (b) at (4,0);
\coordinate (a) at (6,0);
\coordinate (z) at (9,0);
\draw[-{Stealth[]}] (0,0)--(10,0);
\pic at (c){tick=c};
\pic at (b){tick=b};
\pic at (a) {tick=a};
\pic at (z) {tick};
\draw (c) to["2"{draw,circle},my curve] (b) to ["3"{draw,circle},my curve] (a) to ["1"{draw,circle},my curve](z);
\end{tikzpicture}

\end{document}