A vertical line intersects a graph to determine if that graph represents a function, according to the Vertical Line Test.
The vertical line test is a visual method used in mathematics to assess whether a curve plotted on a graph represents a function. Here's a breakdown:
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The Vertical Line Test Explained: Imagine drawing a vertical line anywhere on the graph. If that vertical line intersects the graph at more than one point, then the graph does not represent a function. If the vertical line intersects the graph at only one point (or doesn't intersect it at all), then the graph does represent a function.
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Why this works: A function, by definition, assigns each input (x-value) to exactly one output (y-value). If a vertical line intersects a graph at more than one point, it means that for that particular x-value, there are multiple y-values, thus violating the definition of a function.
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Example: Consider a circle graphed on a coordinate plane. If you draw a vertical line through the middle of the circle, it will intersect the circle at two points (one above the x-axis and one below). Therefore, a circle's graph does not represent a function. However, a straight, non-vertical line will only ever be intersected once by a vertical line and does represent a function.
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In summary: The Vertical Line Test is a quick and easy way to visually determine if a graph represents a function: If any vertical line cuts the graph more than once, it's not a function; otherwise, it is.
