I know that a vertical line has infinite outputs. For that it cannot be a function. What about horizontal lines? Because a horizontal line has only one output.

  • $\begingroup$ We can define functions where the domain is an ordered set of objects and therefore more than one, for example two real numbers. Something which can have many different outs in a domain for the same input is sometimes called a manifold. $\endgroup$ – mathreadler Mar 13 '17 at 8:02

Yup. It represents a function that gives the same output no matter what input you give it. Usually written as $f(x)=a$ (so, for instance, $f(x)=5$ is one such function), and called a constant function.

  • $\begingroup$ and what's the domain of it? $\endgroup$ – Steve Mar 13 '17 at 7:44
  • 3
    $\begingroup$ @Steve Whatever you want it to be. For each domain and each codomain and each point / element in the codomain, there is exactly one constant function with that domain, codomain and output value. $\endgroup$ – Arthur Mar 13 '17 at 7:57

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