This is how a minimal working example of this kind of slides would look like:
% figure and text side by side latex
\documentclass{beamer}
% Theme choice
\usetheme{Berlin}
\begin{document}
\begin{frame}{An archetypical frame}
% start the columns environment
\begin{columns}[c]
% create the column with the text, that occupies half of the slide
\begin{column}{.5\textwidth}
% wrap the text inside a block, so it looks better
\begin{block}{Functions}
The plot with teal color corresponds to the function $y=(x^3-1)^2$ and the plot with red color corresponds to the function $y=(x^{11}-1)^2$
\end{block}
\end{column}
% create the column with the image, that also occupies half of the slide
\begin{column}{.5\textwidth}
% command to actually insert the image
\centering
\includegraphics[scale=0.2]{PlotFunctions.png}
\end{column}
\end{columns}.
\end{frame}
\end{document}
The result of this code looks like what is shown below:

To test the code, you can download the used image: PlotFunctions.PNG.
