Question:
The graphs given alongside represent two functions \(f(x)\) and \(g(x)\) respectively. Which of the following is true?
The graphs given alongside represent two functions \(f(x)\) and \(g(x)\) respectively. Which of the following is true?
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For graph-based function problems, sketch known base graphs (like modulus) and test transformations (reflections, shifts).
Updated On: Jul 29, 2025
- \(g(x) = |f(x)|\)
- \(f(x) = |g(x)|\)
- \(g(x) = -|f(x)|\)
- None of these
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The Correct Option is C
Solution and Explanation
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)
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