The graph of the function \( y = |1 - x| \) consists of two linear segments due to the absolute value function. Here's how it breaks down:

1. For \( x \leq 1 \): The absolute value term becomes \( y = 1 - x \), resulting in a line with a negative slope (-1).
2. For \( x > 1 \): The absolute value term becomes \( y = x - 1 \), resulting in a line with a positive slope (1).

The graph has a V-shape, with the vertex (the point where the two lines meet) at \( (1, 0) \).

Would you like me to generate this graph for you? If so, I can do it right away.

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### 5 Related Questions:
1. How does the graph change if we modify the function to \( y = |x - 1| + 2 \)?
2. What is the slope of each segment of the piecewise linear function \( y = |1 - x| \)?
3. How does the graph of \( y = |x| \) compare to that of \( y = |1 - x| \)?
4. How can you express \( y = |1 - x| \) as a piecewise function?
5. What happens to the graph if we introduce a negative sign, such as \( y = -|1 - x| \)?

**Tip:** When graphing absolute value functions, always look for where the expression inside the absolute value equals zero—this gives you the "turning point" of the V-shape.

Explore the graph of the absolute value function y = |1 - x|, which consists of two linear segments forming a V-shape. Learn how to break down the function into piecewise linear equations and understand the behavior of absolute value functions. Suitable for students in Grades 8-10.

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