Question

What is the equation of the graph?
http://static.k12.com/calms_media/media/330000_330500/330024/1/0f20225bd676adbbbfdd5fb1e3e543d8fa663df6/MS_ALG_S2_01_10_quiz_Q7_question.gif

A. f(x)= -|x-2|
B. f(x)= -|x|+2
C. f(x)= -|x+2|
D. f(x)= -|x|-2

Answer would be great, but an explanation would be awesome!
~Thanks!

Answer 1

if you know the graph of the function |x|, then it'll be ok.

Answer 2

if you have a function \(f\), the graph of the function \(f(x-a)\) is the same as the graph of \(f(x)\) , shifted to the right of \(a\) (it goes to the left if \(a<0\)).
The graph of -\(f(x)\) is the graph of \(f\) reflected