Answer:
B: g(x) = Ix - 4I + 6
Step-by-step explanation:
First, let's describe in a general way the transformations.
Vertical shift.
For a function f(x), a vertical shift of N units is written as:
g(x) = f(x) + N
If N is positive, the shift is upwards
If N is negative, the shift is downwards.
Horizontal shift.
For a function f(x), a horizontal shift of N units is written as:
g(x) = f(x + N)
If N is positive, the shift is to the left.
If N is negative, the shift is to the right.
Now we have the function:
f(x) = IxI
And we first have a shift of 4 units to the right, this is written as:
g(x) = f(x - 4)
Now we have a shift of 6 units up
This is written as:
g(x) = f(x - 4) + 6
Now, knowing that f(x) = IxI, we can write
g(x) = Ix - 4I + 6
Option B.
