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

B vertical translation of 3 units up
C horizontal translation of 3 units right
D vertical translation of 3 units down

Answer 1

D Vertical translation 3 units down

Answer 2

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