Definition of f(x) = |x|
The function f(x) = |x| returns the absolute value of x, which is its distance from zero on the number line. For any real input x, the output is always non-negative.
Range of f(x) = |x|
The range of f(x) = |x| is all real numbers greater than or equal to zero, written as [0, ∞). No matter whether x is positive, negative, or zero, the result is never negative.
Why the Range Starts at Zero
Because absolute value measures distance, the smallest possible output is 0, which occurs when x = 0. As x moves away from zero in either direction, the output increases without bound.
For a concise reference on absolute value functions and their graphs, see Math Is Fun Absolute Value.
