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Example: Verifying the Graph of the Equation y=2x3y = 2x - 3 is a Function

Consider the linear equation y=2x3y = 2x - 3. When plotted on a coordinate plane, its graph forms a straight line. By examining the graph and its accompanying table of values, it is evident that for any given xx-value (input), there is exactly one corresponding yy-value (output). Because every element in the domain maps to exactly one value in the range, the relation defined by the equation y=2x3y = 2x - 3 is mathematically a function. Visually, this is confirmed because any vertical dashed line drawn through the graph intersects the line at only a single point, illustrating the core principle of the vertical line test.

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Updated 2026-05-06

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