Question

The graphs given alongside represent two functions \(f(x)\) and \(g(x)\) respectively. Which of the following is true?

• A. \(g(x) = |f(x)|\)
• B. \(f(x) = |g(x)|\)
• C. \(g(x) = -|f(x)|\)
• D. None of these

Hint:

For graph-based function problems, sketch known base graphs (like modulus) and test transformations (reflections, shifts).

Answer 1

The Correct Option is C

Step 1: Analyze the graphs 
From the left graph (for \(f(x)\)): 

Looks like a “V”-shaped graph opening upward → Suggests \(f(x) = |x|\) From the right graph (for \(g(x)\)): 

“V”-shaped graph opening downward → Suggests \(g(x) = -|x|\)

Step 2: Compare definitions If \(f(x) = |x|\), then clearly: \[ g(x) = -|x| = -|f(x)| \Rightarrow g(x) = -|f(x)| \] % Final Answer: (c)