The equation $|x - 1| = -2$ has no solution. This is because the absolute value of a number is always non-negative (i.e., greater than or equal to zero). It can never be negative, like $-2$.

Explanation:

1. The absolute value of any expression, such as $|x - 1|$, represents the distance of that expression from zero, which is always zero or positive.
2. Since no value of $x$ can make $|x - 1|$ equal to $-2$, there are no $x$-values to graph.

Therefore, there is no graph for this equation as it has no real solutions.

Questions for Further Exploration:

1. What are the properties of absolute value functions?
2. How do you solve absolute value equations like $|x + 3| = 5$?
3. What is the graphical interpretation of an absolute value function?
4. How can you graph absolute value inequalities?
5. What happens if you change $|x - 1| = -2$ to $|x - 1| = 2$?

Tip: Absolute value equations can only have real solutions when set equal to a non-negative value.