$\"\"$

The parent function is $\"\"$ .

Find the transformation function.

General form of the transformations of exponential functions is $\"\"$ .

Here,

$\"\"$ is Horizontal translation.

$\"\"$ is Vertical translation.

$\"\"$ is Orientation and shape.

Observe the graph:

Consider the scale on the graph about $\"\"$ and $\"\"$ -axis is $\"\"$ .

The graph translated $\"\"$ units up.

The graph is reflected about $\"\"$ -axis and compressed vertically.

Here $\"\"$ and $\"\"$ .

$\"\"$ (Substitute $\"\"$ and $\"\"$ )

Therefore, the transformation function is $\"\"$ .

$\"\"$

The transformation function is $\"\"$ .