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Encyclopedia > Horizontal line test

In mathematics, the horizontal line test is a test used to determine if a function is injective, surjective or bijective.


Suppose there is a function f : X → Y with a graph., and you have a horizontal line of X x Y : .

  • If the function is injective, then it can be visualized as one whose graph is never intersected by any horizontal line more than once.
  • Iff f is surjective any line will intersect the graph at least at one point
  • iff f is bijective any line will intersect the graph at exactly one point.

Image:Horizontal-test-ok.png

Succeeds the test (injective)

Image:Horizontal-test-fail.png

Fail the test (not injective)

  Results from FactBites:
 
Horizontal and Vertical Line Tests - Wolfram Demonstration Project (0 words)
If no horizontal line intersects the function in more than one point, it is one-to-one (or injective).
If every horizontal line intersects the function in at least one point, it is onto (or surjective).
If every horizontal line intersects the function in exactly one point, it is one-to-one and onto (or bijective).
  More results at FactBites »


 

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