Can't find a proper right-curved, non-continuous function

Hi everyone! I should reproduce these plots (above) and I'm so far that I have everything except for the plots themselves. Does anyone here have an idea what kind of plots should I take? I'm not a math-pro and google couldn't help me either.

Here the code and what I've got so far (this is my first question and I don't know why the formatting of the code doesn't work, sorry for that):

    \documentclass{standalone}

\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
restrict y to domain=-5:5,
samples=1000,
ticks=none,
xmin = -1, xmax = 5,
ymin = -1, ymax = 5,
unbounded coords=jump,
axis x line=middle,
axis y line=middle,
x label style={
at={(axis cs:5.02,0)},
anchor=west,
},
every axis y label/.style={
at={(axis cs:0,5.02)},
anchor=south
},
legend style={
at={(axis cs:-5.2,5)},
anchor=west, font=\scriptsize
}
]

\draw[dashed] (axis cs:2,0) -- (axis cs:2,2);
\draw[dashed] (axis cs:0,2) -- (axis cs:2,2);
\node[below right, font=\scriptsize] at (axis cs:2,0) {$a$};
\node[below right, font=\scriptsize] at (axis cs:2,4) {$stetig$};
\node[above left, font=\scriptsize] at (axis cs:0,2) {$f(a)$};
\end{axis}
\end{tikzpicture}

\begin{tikzpicture}
\begin{axis}[
restrict y to domain=-5:5,
samples=1000,
ticks=none,
xmin = -1, xmax = 5,
ymin = -1, ymax = 5,
unbounded coords=jump,
axis x line=middle,
axis y line=middle,
x label style={
at={(axis cs:5.02,0)},
anchor=west,
},
every axis y label/.style={
at={(axis cs:0,5.02)},
anchor=south
},
legend style={
at={(axis cs:-5.2,5)},
anchor=west, font=\scriptsize
}
]

\draw[dashed] (axis cs:2,0) -- (axis cs:2,2);
\draw[dashed] (axis cs:0,1) -- (axis cs:2,1);
\draw[dashed] (axis cs:0,2) -- (axis cs:2,2);
\node[below right, font=\scriptsize] at (axis cs:2,0) {$a$};
\node[below right, font=\scriptsize] at (axis cs:2,4) {$nicht \; stetig$};
\node[above left, font=\scriptsize] at (axis cs:0,2) {$f(a)$};
\end{axis}
\end{tikzpicture}
\end{document}


• This seems more math than LaTeX/PgfPlots question ... – Zarko Feb 13 '16 at 13:46

Since the drawing is about continuity and discontinuity, there's no need to exactly plot specifically these functions. You could use any continuous and discontinuous functions. You could even make a coordinates plot with smooth path between.

But let's find a function based on your coordinates. The drawing looks like made of pieces of a circle, so let's use a function which can give us a circle, and limit its domain.

First plot:

\addplot [no markers, domain=1.3:4] { sqrt(8-(x-4)^2)};


For the second plot, we plot the function two times, but shift it the second time, again with limited domains.

\addplot [no markers, domain=1.3:2] { -sqrt(8-(x)^2)+3};
\addplot [no markers, domain=2:2.8] { -sqrt(8-(x)^2)+4};


We get:

• Thank you very much! This is exactly what I wanted. Special thanks to the good explanation! – Latex beginner Feb 13 '16 at 19:05