Which graph shows the transformation of the function f(x) = e^x where the function is translated three units to the right, vertically compressed by a factor of 1/4, and then translated six units down.

C is correct graph.

Step-by-step explanation:

Given:

Now we do some operation on function f(x)

Step 1: f(x) is translated 3 units to the right.

For a unit right translation, x changes to

Therefore,

Step 2: Vertical compressed by a factor of

For vertical compressed. f(x) changes to a f(x)  

Step 3: Translated 6 unit down

For this translation, y changes to

Therefore,

Final function after three steps we get,

Please see the attachment for correct graph.

Thus, C is correct graph.

step-by-step explanation: