b We are given the following absolute value equation.
y=|x|+3
The above function is a transformation of the parent function y=|x|. Notice that this is a vertical translation 3 units up. As a result, the graph of y=|x| becomes y=|x|+3.
As we can see, this graph corresponds to Graph 1.
c We are given the following absolute value equation.
y=|x-1|+3
The above function is a transformation of the parent function y=|x|. Let's look at each of the transformations individually. First we will do a horizontal translation 1 unit to the right. This will transform the graph of the parent function, y=|x|, to the graph of y=|x-1|.
Now, let's do a vertical translation 3 units up. As a result, the graph of y=|x-1| becomes y=|x-1|+3.
As we can see, the final graph corresponds to Graph 2.
