Exercise 33 Page 17

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. 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.