We are given the absolute value function

f (x) = ∣ x ∣ .

The function is shifted 3 units right and 2 units up. In order to get the function rule of the translated function, we will use translation rules. Graph translations follow the formula below, where

h

represents horizontal translation and

k

represents vertical translation.

g (x) = f (x - h) + k

Positive

k

values shift the function up, and negative

k

values shift it down. Similarly, positive

h

values shift the function right, and negative

h

values shift it left. However, there is a minus sign in the formula in front of

h

, so the sign in the function rule is always opposite the sign of

h .

Let's execute the given translations. Since

f (x) = ∣ x ∣,

g (x) = ∣ x - h ∣ + k .

g (x) = ∣ x - h ∣ + k

SubstituteII

$h = 3$ , $k = 2$

g (x) = ∣ x - 3 ∣ + 2

We can see that the only difference between our function and the function

g (x) = ∣ x + 3 ∣ + 2

from the exercise is the minus sign in front of

3

. Thus, we can assume that whoever wrote it forgot about minus sign in the translation rule formula.

Exercise