Graph of y = |x|
Interactive graph of y = |x| (absolute value of x). Explore the V-shaped graph, its vertex, and piecewise linear behavior with our free graphing calculator.
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Understanding the Function
The absolute value function y = |x| produces a V-shaped graph with its vertex at the origin. For positive x, the function equals x; for negative x, it equals -x. This makes it one of the simplest piecewise-defined functions and a fundamental example in real analysis.
The absolute value function is even, meaning |−x| = |x|, giving it perfect symmetry about the y-axis. It is continuous everywhere but not differentiable at x = 0, where the graph has a sharp corner. This makes it an important example when discussing limits, derivatives, and the distinction between continuity and differentiability.
Key properties: vertex at (0, 0), slope of -1 for x < 0 and slope of 1 for x > 0, domain of all real numbers, range of [0, infinity). The function is used extensively in distance calculations, error measurement, and optimization with L1 norms.