When the graph of the function $f ( x ) = 2 ^ { x }$ is translated by $m$ in the $x$-direction and by $n$ in the $y$-direction, the graph of the function $y = g ( x )$ is obtained. By this translation, point $\mathrm { A } ( 1 , f ( 1 ) )$ moves to point $\mathrm { A } ^ { \prime } ( 3 , g ( 3 ) )$. When the graph of the function $y = g ( x )$ passes through the point $( 0,1 )$, what is the value of $m + n$? [3 points] (1) $\frac { 11 } { 4 }$ (2) 3 (3) $\frac { 13 } { 4 }$ (4) $\frac { 7 } { 2 }$ (5) $\frac { 15 } { 4 }$
When the graph of the function $f ( x ) = 2 ^ { x }$ is translated by $m$ in the $x$-direction and by $n$ in the $y$-direction, the graph of the function $y = g ( x )$ is obtained. By this translation, point $\mathrm { A } ( 1 , f ( 1 ) )$ moves to point $\mathrm { A } ^ { \prime } ( 3 , g ( 3 ) )$. When the graph of the function $y = g ( x )$ passes through the point $( 0,1 )$, what is the value of $m + n$? [3 points]\\
(1) $\frac { 11 } { 4 }$\\
(2) 3\\
(3) $\frac { 13 } { 4 }$\\
(4) $\frac { 7 } { 2 }$\\
(5) $\frac { 15 } { 4 }$