How to format table with images?

Question

How to format this table? I do not know how to handle the images...

\begin{table}[h]
    \centering
    \begin{tabular}{llll}
        \hline
        \multicolumn{1}{l}{Name} & \multicolumn{1}{l}{Function} & \multicolumn{1}{l}{Derivative} & \multicolumn{1}{l}{Figure} \\ \hline
        Sigmoid & $\sigma(x)=\frac{1}{1+e^{-x}}$ & $f'(x)=f(x)(1-f(x))^2$  &  \includegraphics[width=0.2\textwidth]{sigmoid}\\
        tanh & $\sigma(x)=\frac{e^x-e^{-x}}{e^z+e^{-z}} $ & $f'(x)=1-f(x)^2$   &  \includegraphics[width=0.2\textwidth]{tanh} \\
        ReLU & $f(x) \left\{\begin{matrix}
        0 & if \; x<0 \\ 
        x &  if \;x \geq 0.
        \end{matrix}\right.$ & $f(x) \left\{\begin{matrix}
        0 & if \; x<0 \\ 
        x &  if \;x \geq 0.
        \end{matrix}\right.$ & \includegraphics[width=0.2\textwidth]{relu} \\
        Softmax & $f(x)=\frac{e^x}{\sum_i e^x}$ & $f'(x)=\frac{e^x}{\sum_i e^x} - \frac{(e^x)^2}{(\sum_i e^x)^2}$ &                            
    \end{tabular}
    \caption{Non-linear activation functions.}
    \label{tab:activationfct}
\end{table}

The current output looks like this:

These are the images in the table:

[

Answer 1

I'd like to argue that it is more fun to draw these functions with TikZ. You'll then have full control over the vertical placement with baseline, as I illustrate below, and if you decide to add axis labels etc. they'll have the same fonts and appearance. And I used the opportunity to fix a few typos and to use cases where appropriate. Note also that you can use scale to make the plots larger.

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{table}[h]
\centering
\begin{tabular}{llll}
    \hline
    \multicolumn{1}{l}{Name} & \multicolumn{1}{l}{Function} & \multicolumn{1}{l}{Derivative} & \multicolumn{1}{l}{Figure} \\ 
    \hline
    Sigmoid & $\sigma(x)=\frac{1}{1+e^{-x}}$ & $f'(x)=f(x)(1-f(x))^2$  &  
    \begin{tikzpicture}[baseline={(0,0.2)}]
     \draw (-1,0) -- (1,0);
     \draw (0,0) -- (0,1);
     \draw plot[domain=-1:1,variable=\x] ({\x},{1/(1+exp(-4*\x))});
    \end{tikzpicture}\\
    \\
    tanh & $\sigma(x)=\frac{e^x-e^{-x}}{e^z+e^{-z}} $ & $f'(x)=1-f(x)^2$   
    &  \begin{tikzpicture}[baseline={(0,0)}]
     \draw (-1,0) -- (1,0);
     \draw (0,-1) -- (0,1);
     \draw plot[domain=-1:1,variable=\x] ({\x},{tanh(4*\x)});
    \end{tikzpicture} \\
    ReLU & $f(x) =\begin{cases}
    0 & ~\text{if}~ x<0 \\ 
    x & ~\text{if}~x \geq 0.
    \end{cases}$ & $f'(x)=\begin{cases}
    0 & ~\text{if}~ x<0 \\ 
    x & ~\text{if}~1 \geq 0.
    \end{cases} $ & 
    \begin{tikzpicture}[baseline={(0,0.5)}]
     \draw (-1,0) -- (1,0);
     \draw (0,0) -- (0,1);
     \draw plot[domain=-1:1,variable=\x] ({\x},{ifthenelse(\x<0,0,\x)});
    \end{tikzpicture}\\
    Softmax & $f(x)=\frac{e^x}{\sum_i e^x}$ & $f'(x)=\frac{e^x}{\sum_i e^x} - \frac{(e^x)^2}{(\sum_i e^x)^2}$ &                            
\end{tabular}
\caption{Non-linear activation functions.}
\label{tab:activationfct}
\end{table}
\end{document}

Answer 2

adopted my answer to your code fragment (your question is duplicate, however since your code fragment has some off-topic issues, see mwe below i wrote this answer):

\documentclass{scrreprt}
\usepackage[export, demo]{adjustbox}    % in real document delete option "demo"
                                        % adjustbox call "graphicx"
                                        % "adjustbox" call "graphicx" plus add many function
                                        % for manipulating boxes, among them here is used "valign"
\usepackage{cellspace,                  % for adding vertical space around cells' contents
            tabularx}
\setlength\cellspacetoplimit{4pt}
\setlength\cellspacebottomlimit{4pt}
\addparagraphcolumntypes{X}
\usepackage{ragged2e}
\usepackage{amsmath} % added

\begin{document}

\begin{table}[htb]
    \centering
\setkeys{Gin}{width=0.2\textwidth}   % with real images should be sufficient defined only image width
\begin{tabular}{l *{2}{>{$\displaystyle}Sl<{$}} Sl} % changed
        \hline
{Name}      & {Function}
                & {Derivative}
                    & {Figure}                      \\
        \hline
Sigmoid & \sigma(x)=\frac{1}{1+e^{-x}}
            & f'(x)=f(x)(1-f(x))^2
                &  \includegraphics[valign=c]{sigmoid}        \\
tanh    & \sigma(x)=\frac{e^x-e^{-x}}{e^z+e^{-z}}
            & f'(x)=1-f(x)^2
                &  \includegraphics[valign=c]{tanh}           \\
ReLU    & f(x) \begin{cases} % changed and corrected
                    0 & if \; x<0 \\
                    x &  if \;x \geq 0.
                \end{cases}
            & f(x) \begin{cases} % changed and corrected
                        0 & if \; x<0 \\
                        x &  if \;x \geq 0.
                    \end{cases}
                & \includegraphics[valign=c]{relu}            \\
Softmax & f(x)=\frac{e^x}{\sum_i e^x}
            & f'(x)=\frac{e^x}{\sum_i e^x} - \frac{(e^x)^2}{(\sum_i e^x)^2}
                &                                   \\
    \hline
\end{tabular}
    \caption{Non-linear activation functions.}
    \label{tab:activationfct}
\end{table}
\end{document}