You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: The figure shows graphs of functions $f$ and $g$ defined on real numbers. Each graph consists of two perpendicular halflines. Which equality is satisfied for every real number $x$?
<image1>
Choices:
(A) $f(x)=-g(x)+2$
(B) $f(x)=-g(x)-2$
(C) $f(x)=-g(x+2)$
(D) $f(x+2)=-g(x)$
(E) $f(x+1)=-g(x-1)$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
C
Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: The figure shows graphs of functions $f$ and $g$ defined on real numbers. Each graph consists of two perpendicular halflines. Which equality is satisfied for every real number $x$?
<image1>
Choices:
(A) $f(x)=-g(x)+2$
(B) $f(x)=-g(x)-2$
(C) $f(x)=-g(x+2)$
(D) $f(x+2)=-g(x)$
(E) $f(x+1)=-g(x-1)$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val