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The graph of \( |f(x)| = |x - 5| \) shows an absolute value function, which creates a "V" shape. As \( x \) approaches 5, the value of \( |f(x)| \) approaches zero, because \( |5 - 5| = 0 \). This illustrates the limit \(\lim_{x \to 5} |f(x)| = 0\).

Let me know if you need any further clarification, or if you want to explore specific details!

Here are five related questions for practice:
1. What is the limit of \( |f(x)| \) as \( x \to 5 \) from the left and right?
2. How would the graph change if the function was \( |x - 3| \) instead?
3. What is the derivative of \( |x - 5| \) for \( x \neq 5 \)?
4. Can you explain why the function is continuous at \( x = 5 \)?
5. How does the absolute value affect the slope on either side of \( x = 5 \)?

**Tip:** For absolute value functions, the slope changes at the point where the expression inside the absolute value equals zero!

Learn how to solve the limit lim(x -> 5) |f(x)| with a detailed step-by-step explanation. This problem involves key calculus concepts such as limits, absolute value functions, and the continuity theorem. Suitable for high school students in Grades 11-12.

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