We want to find the equation of a transformed graph of an absolute value function. The parent function in this case is y=|x-1|. We are given that the graph is translated 4 units up and 3 units right. Let's first consider the general form of an absolute value function.
y= a|x- h|+ k
In this form, each of the constants represents one of the three basic types of transformations.
With this in mind, we can see that k and h from the general form are the values that are of interest to us. The vertical translation 4 units up will go where k goes.
y=|x-1|+ 4
Now, let's consider the horizontal translation. We want to translate the graph 3 units right, so h is equal to 3.
y=|x-1- 3|+4
Note that, in our case, the parent function already had a subtraction inside the absolute value. Therefore, to translate this function 3 units to the right, we need to subtract 3 from the whole expression in the absolute value symbols. Finally, let's simplify the obtained equation.
y=|x-1-3|+4
⇕
y=|x-4|+4
This corresponds to option G.
