Discuss the continuity of the function f given by `f(x) = |x| a t x = 0`.

Explanation

To discuss the continuity of the function \( f(x) = |x| \) at \( x = 0 \), we will follow the definition of continuity. A function is continuous at a point \( c \) if the following three conditions are satisfied:

1. \( f(c) \) is defined.
2. The limit \( \lim_{x \to c} f(x) \) exists.
3. \( \lim_{x \to c} f(x) = f(c) \).

Let's apply these steps to our function at \( x = 0 \).

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