Final answer:
To vertically stretch the function f(x)=((1)/(2))ˣ by a factor of 3, shift it 4 units to the right, and down 2 units, the transformed function would be f(x) = 3 * ((1/2)^(x-4)) - 2.
Step-by-step explanation:
To vertically stretch a function by a factor of 3, you multiply the function by 3. To shift the graph to the right by 4 units, you subtract 4 from the x-values. To shift the graph down by 2 units, you subtract 2 from the y-values. The transformed function would be f(x) = 3 * ((1/2)^(x-4)) - 2.