Answer:
Option D.
Step-by-step explanation:
It is given that, graph of j(x) transformed in the graph of j(4x) – 27.
We need to find the transformations.
Consider the new function is
... (1)
The translation is defined as
... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph stretched horizontally by factor of 1/k and if k>1, then the graph compressed horizontally by factor of 1/k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
k=4>1, the graph j(x) compressed horizontally by factor of 1/4.
a=0, so there is no horizontal shift.
b=-27<0, so the graph of j(x) shifts 27 units down.
So, the required transformations are horizontal compression by a factor of 1/4, and a translation 27 units down.
Therefore, the correct option is D.