The vertex of an absolute value function is precisely defined as the distinct point on its graph where the straight line changes its slope, forming the function's characteristic V-shape. For the basic absolute value function $$f(x) = |x|$$, this vertex point is located exactly at the origin $$(0, 0)$$.

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The absolute value function is fundamentally defined by the equation $$f(x) = |x|$$. Because the absolute value can be cleanly computed for any real input, its domain is all real numbers, expressed as $$(-\infty, \infty)$$. However, since absolute value represents a number's physical distance from zero, the output can never be negative. Therefore, the range is strictly restricted to non-negative real numbers, or $$[0, \infty)$$. Geometrically, the graph of this function creates a sharp, symmetrical V-shape that consists of two linear rays converging exactly at the origin $$(0, 0)$$.

Absolute Value Function

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