Question

What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=−3+|x|? A horizontal translation of 3 units left

Answer 1

There are 4 possible translations of the parent function $f(x)=|x|:$

1. a units to the right - the function will become $f(x)=|x-a|;$
2. a units to the left - the function will become $f(x)=|x+a|;$
3. a units up - the function will become $f(x)=|x|+a;$
4. a units down - the function will become $f(x)=|x|-a.$

Now you have the function $g(x)=-3+|x|=|x|-3$ that is translated  function $f(x)=|x|$ 3 units down.

Answer: correct choice is D

Answer 2

D Vertical translation 3 units down