• Functions are a type of relations, so all functions are relations but not all relations are functions.
  • Relations can be any two number pairs, but functions are different.
  • For every input number, there is only one output. But one output number can have multiple inputs.
  • For example, if the coordinates are (1,4)(2,6) (3,4) that is a function, but if the coordinates are (3, 7) (6, 8) (3, 5) that is not a function since 3 has 2 different outputs.
  • Another way to check for functions is a vertical line test. This is used when you have a graph, you can imagine a vertical line going across the graph, and if it ever comes across 2 points at once, it is a relation and NOT A FUNCTION.
  • If the vertical line goes across the graph and never touches 2 points at once, then it is a function.
  • Here is an example of a function:

Image result for function graph

  • And this is not a function:

Image result for non function relation graph

 

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