Question

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

vertical translation of 3 units down

vertical translation of 3 units up

horizontal translation of 3 units right

horizontal translation of 3 units left

Answer 1

vertical translation of 3 units down

Explanation:

we have

`f\left(x\right)=\left|x\right|`

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

`g\left(x\right)=-3+\left|x\right|`

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

see the attached figure to better understand the problem

so

The transformation of f(x) to g(x) is

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

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

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

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

therefore

vertical translation of 3 units down