1. Horizontal translation of 2 units to the right.
2. Vertical shift up 1 unit.
3. vertical shift down 3 units:
4. horizontal translation 3 units to the left
1) We can see that these functions are actually transformed versions of the parent function f(x)=|x|
2) So examining each one we can state the following:
1.
[tex]g(x)=|x-2|[/tex]Note that this function is a horizontal translation of 2 units to the right.
2. The following function, on the other hand, with the +1 outside the absolute value bars is a vertical shift or vertical translation up 1 unit.
[tex]g(x)=|x|+1[/tex]3. Similarly, we can see that this one presents a vertical shift down 3 units:
[tex]g(x)=|x|-3[/tex]4. Finally, in this last one, we have a horizontal translation 3 units to the left:
[tex]g(x)=|x+3|[/tex]Thus the answer is:
1. Horizontal translation of 2 units to the right.
2. Vertical shift up 1 unit.
3. vertical shift down 3 units:
4. horizontal translation 3 units to the left