What exponential function have all these attributes
- 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 \(y = ab^{(x-h)} + k\), 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.

Step 3 ：However, we also need to ensure that the range is \(y > 3\). This means that the vertical shift, \(k\), must be 3.

Step 4 ：So, the function should be \(y = \frac{1}{4} \cdot 2^{(x-1)} + 3\).

Step 5 ：The plot of the function \(y = \frac{1}{4} \cdot 2^{(x-1)} + 3\) shows that the function has the correct attributes. The domain is all real numbers, the range is \(y > 3\), the base is 2, and the function has a vertical compression of 1/4 and a horizontal shift to the right by 1.

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