Chapter 1 - Limits and Continuity - 1.5 Continuity - Exercises Set 1.5 - Page 99: 23

True

If $f(c)\geq 0$, then the function remains the same and remains continuous. If $f(x) < 0$, each and every point is reflected along the x-axis. Reflection preserves continuity as if a function $f(x)$ is continuous, so $-f(x)$ is similarly continuous. Thus $|f(x)|$ is continuous.