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Example: Verifying the Graph of the Equation is a Function
Consider the linear equation . 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 -value (input), there is exactly one corresponding -value (output). Because every element in the domain maps to exactly one value in the range, the relation defined by the equation 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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Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
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Example: Determining if a Graphed Straight Line and a Horizontal Parabola Represent a Function Using the Vertical Line Test
Example: Determining if a Graphed Vertical Parabola and a Circle Represent a Function Using the Vertical Line Test
Example: Determining if a Graphed Ellipse and a Slanted Line Represent a Function Using the Vertical Line Test
Example: Verifying the Graph of the Equation is a Function