Question

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.

Answer 1

C is correct graph.

Explanation:

Given:
`f(x)=e^x`

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

`x\rightarrow x-a`

Therefore,
`f(x)=e^(x-3)`

Step 2: Vertical compressed by a factor of
`(1)/(4)`

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

`f(x)=(1)/(4)e^(x-3)`

Step 3: Translated 6 unit down

For this translation, y changes to

`y\rightarrow y-6`

Therefore,
`f(x)=(1)/(4)e^(x-3)-6`

Final function after three steps we get,

`f(x)=(1)/(4)e^(x-3)-6`

Please see the attachment for correct graph.

Thus, C is correct graph.