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Example: Determining if a Graphed Straight Line and a Horizontal Parabola Represent a Function Using the Vertical Line Test

To determine whether a graph represents a mathematical function, apply the vertical line test. For example, consider the graph of a slanted straight line. Because any vertical line drawn anywhere on the coordinate plane intersects this straight line at exactly one point, the graph passes the test and represents a function. In contrast, consider the graph of a sideways parabola that opens to the right (a horizontal parabola). A vertical line can be drawn that passes through two distinct points on this curve. Because a single vertical line intersects the graph more than once, it indicates that one xx-value corresponds to multiple yy-values. Therefore, the horizontal parabola fails the vertical line test and does not represent a function.

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Updated 2026-05-06

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