Bergen

2021-08-12

How many times can a horizontal line intersect the graph of a function that is one-to-one?

toroztatG

Skilled2021-08-13Added 98 answers

Suppose f is an one-to-one function.

If (a,b) lies in the graph of f, then there does not exists any x with x!=a such that (x,b) also lies in the graph of f (because f is one-to-one).

This means if f is one-to-one, then a horizontal line intersect the graph of f at most once.

Thus a horizontal line intersect the graph of an one-to-one function at most once.

If (a,b) lies in the graph of f, then there does not exists any x with x!=a such that (x,b) also lies in the graph of f (because f is one-to-one).

This means if f is one-to-one, then a horizontal line intersect the graph of f at most once.

Thus a horizontal line intersect the graph of an one-to-one function at most once.

RizerMix

Expert2023-06-14Added 656 answers

Don Sumner

Skilled2023-06-14Added 184 answers

Vasquez

Expert2023-06-14Added 669 answers

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