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 . 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.
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.