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.