Which exponential function has the following characteristics
- Domain: all real numbers
- Range: y> 3
- Base: 2
- Additional Transformations: vertical compression of 1/4, horizontal shift right 1

Step 1 ：The general form of an exponential function is \(y = a*b^{(x-h)} + k\), where \(a\) is the vertical stretch/compression, \(b\) is the base, \(h\) is the horizontal shift, and \(k\) is the vertical shift.

Step 2 ：Given that the base is 2, the vertical compression is 1/4, and the horizontal shift to the right is 1, we can substitute these values into the general form to get \(y = \frac{1}{4}*2^{(x-1)} + k\).

Step 3 ：However, we also know that the range is \(y>3\), which means the function must always be greater than 3. This implies that the vertical shift, \(k\), must be greater than 3.

Step 4 ：Since the question does not specify a specific value for \(k\), we can choose any value greater than 3. For simplicity, let's choose \(k = 3\).

Step 5 ：So, the function that meets all these characteristics is \(y = \frac{1}{4}*2^{(x-1)} + 3\).

Step 6 ：Final Answer: The exponential function that has the given characteristics is \(\boxed{y = \frac{1}{4} \cdot 2^{(x-1)} + 3}\).