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: