Question

What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=−3+|x|?

Answer 1

Answer:

vertical translation of 3 units down

Step-by-step explanation:

we have

$f\left(x\right)=\left|x\right|$ ----> the parent function

The vertex of f(x) is the point (0,0)

$g\left(x\right)=-3+\left|x\right|$ ----> the transformed function

The vertex  of g(x) is the point (0,-3)

so

The rule of the translation is

f(x) -----> g(x)

(0,0) ----> (0,-3)

(x,y) ----> (x,y-3)

That means ---> The translation is 3 units down

see the attached figure to better understand the problem