Consider the function $f: \{2, 3, 6, 7, 9\} \to \{1, 2, 5, 6, 7, 9\}$ given by the table below:
\begin{tabular}{c|ccccc}
$x$ & 2 & 3 & 6 & 7 & 9 \\
$f(x)$ & 5 & 1 & 2 & 2 & 1
\end{tabular}
a. Is $f$ injective? Why or why not?
\begin{itemize}
\item Yes, because every element in the codomain is the image of at most one element of the domain.
\item No, because at least one element in the codomain is the image of two or more elements of the domain.
\item Yes, because every element in the codomain is the image of at least one element of the domain.
\item No, because at least one element in the codomain is not the image to an element of the domain.
\end{itemize}
b. Is $f$ surjective? Why or why not?
\begin{itemize}
\item Yes, because every element in the codomain is the image of at most one element of the domain.
\item No, because at least one element in the codomain is the image of two or more elements of the domain.
\item Yes, because every element in the codomain is the image of at least one element of the domain.
\item No, because at least one element in the codomain is not the image to an element of the domain.
\end{itemize}
