Discuss the continuity of the `f(x)` at the indicated point: `f(x)=|x|+|x-1|` at `x=0,\ 1` .

Explanation

To determine the continuity of the function \( f(x) = |x| + |x - 1| \) at the points \( x = 0 \) and \( x = 1 \), we need to check the following conditions for continuity at each point:

1. The function \( f(x) \) is defined at the point.
2. The limit of \( f(x) \) as \( x \) approaches the point exists.
3. The limit of \( f(x) \) as \( x \) approaches the point is equal to the value of the function at that point.

Let's analyze the function at both points step by step.

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