The absolute value of a number is the distance of the number from zero, meaning that the absolute values of 6 and -6 are 6. Because the argument of an absolute value function may be positive or negative, we have to satisfy both cases: when x > 0 and x < 0.

Why does the limit not exist for absolute value?

So, for example, take the absolute value function f(x) = |x| and restrict it to the closed interval [−1, 2]. ... Likewise, at x = 2, the left limit of the difference quotient exists, but the function is undefined to the right of x = 2, so the right limit does not exist.

Do absolute value functions have minimums?

The range consists of just two y-values: {−1,1}. The function f is constant on (−∞,0) and (0,∞). The local minimum value of f is the absolute minimum value of f, namely −1; the local maximum and absolute maximum values for f also coincide − they both are 1.