Answer
The possible equation for the given graph is $y=\sqrt{x-2}+1$.
Work Step by Step
The above given graph looks similar to the graph of the function $y=\sqrt{x}$, but the graph of $y=\sqrt{x}$ passes through the origin. So this graph should be called the shifted graph.
The graph is right-shifted by unit $c$. Therefore, the variable $x$ is replaced by the factor $x-c$.
So, the equation is:
$\begin{align}
& y=\sqrt{x} \\
& =\sqrt{x-c}
\end{align}$
It can be clearly observed from the graph, that the value of $c$ is 2.
So,
$\begin{align}
& y=\sqrt{x-c} \\
& =\sqrt{x-2}
\end{align}$
Further the graph is shifted upwards vertically on the $y$ axis with unit 1.
Then,
$\begin{align}
& y=\sqrt{x-2} \\
& =\sqrt{x-2}+1
\end{align}$
Hence, the graph of the function is in the form of $y=\sqrt{x-c}+a$.
Where $c=2,a=1$.
Hence, the possible function is $y=\sqrt{x-2}+1$.
