# 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.

Original function is f(x) =

For this y intercept = 1. i.e. passes through (0,1)

First it is translated three units to the right.

So y =

When vertically compressed by a factor of 1/4 we have

y =

Next is translated 6 units down

i.e. new graph would be

y = +6

When x =3, y =6.

When y =-6, x tends to infinity.

i.e. y =-6 is an asymptote

Hence we find that 4th graph is the correct answer.

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.