Question

If you apply the changes below to the absolute value parent function, f(x) = [xl,

what is the equation of the new function?
• Shift 4 units to the right.
Shift 6 units up.
A. g(x) = |x-6] + 4
B. g(x) = 5x – 4[ + 6
C. g(x) = 5x + 4[ + 6
D. g(x) = 5x + 6 + 4

Answer 1

B: g(x) = Ix - 4I + 6

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.