On the coordinate plane, the graph of the exponential function $y = a ^ { x }$ is reflected about the $y$-axis, then translated 3 units in the $x$-direction and 2 units in the $y$-direction. The resulting graph passes through the point $( 1,4 )$. What is the value of the positive number $a$? [3 points]\\
(1) $\sqrt { 2 }$\\
(2) 2\\
(3) $2 \sqrt { 2 }$\\
(4) 4\\
(5) $4 \sqrt { 2 }$