Chapter 1 - Limits and Continuity - 1.5 Continuity - Exercises Set 1.5 - Page 99: 24

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To transform $|f(x)|$ to $f(x)$, we must reflect certain points across the x-axis. However, it is not given which points must be reflected, and it is possible that only $f(c)$ needs reflecting across the x-axis. This would then break continuity, showing that $f(x)$ is not necessarily continuous.