Horizontal Line Test
The horizontal line test is a technique used to determine if a function is one-to-one or many-to-one
The horizontal line test is a technique used to determine if a function is one-to-one or many-to-one. It is a visual test that involves analyzing the intersection points between a function and horizontal lines.
To perform the horizontal line test, you need to graph the function on a coordinate plane. Then, for each horizontal line drawn on the graph, observe how many times the line intersects the graph.
If every horizontal line intersects the function’s graph at most once, and no two points on the graph share the same y-coordinate, then the function passes the horizontal line test. This means that the function is one-to-one, or injective, indicating that each input value is associated with a unique output value.
On the other hand, if you can find a horizontal line that intersects the graph at two or more points, it fails the horizontal line test. This indicates that the function is many-to-one, or not injective, meaning that multiple input values may yield the same output value.
This test is particularly useful in analyzing functions that are represented graphically, as it provides an intuitive way to determine the injectivity of a function.
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