Answer:
f(x - 4) - 9
Explanation:
The exact value of f(x) is missing, but I can give a general answer, which can be changed for any value of f(x).
Following transformation is applied on the function f(x):
9 spaces down and 4 spaces to the right.
This is a combinations of 2 transformations:
1) 9 spaces down:
This is a vertical translation. Vertical translation of f(x) is represented as:
f(x) + k
Here, k represents the number of units(spaces) by which f(x) is translated vertically. A positive value of k means upward translation and a negative value means downward translation. So, if we want to move f(x) 9 spaces down, the resulting expression will be:
f(x) + (-9) = f(x) - 9
So, in order to shift a function 9 units(spaces) down, simply subtract 9 from the function value.
2) 4 spaces to right:
This is a horizontal translation. Horizontal translation of f(x) is represented as:
f(x + C)
Here, C represents the number of units(spaces) by which f(x) is translated horizontally. A positive value of C means leftwards translation and a negative value of C means rightward translation. So, if we want to move f(x) by 4 spaces(units) to right, the expression will be:
f(x + (-4)) = f(x - 4)
So, in order to shift the function 4 units(spaces) to right, replace every occurrence of x by x - 4.
Combining both the transformations, the resulting expression will be:
f(x - 4) - 9
This is the expression after translation f(x) 9 spaces down and 4 spaces to the right.