Ans: C
Consider the general case $g(x)=f(x+h)+k$.
Consider the general case $g(x)=f(x+h)+k$.
If $h$ is positive, then the graph of $f(x)$ translates to the left $h$ units. If $h$ is negative, the graph of $f(x)$ translates to the right $-h$ units.
If $k$ is positive, then the graph of $f(x)$ translates upwards $k$ units. If $k$ is negative, the graph of $f(x)$ translates downwards $-k$ units.
According to the vertex of the graph in the given figure, the graph of $f(x)$ translates to the left $2$ units and downwards $3$ units.
Therefore $h=2$ and $k-3$.
Hence, $g(x)=f(x+2)-3$.
