Question

Suppose $f$ is the collection of all ordered pairs of real numbers and $x=6$ is the first element of some ordered pair in $f$. Suppose the vertical line through $x=6$ cuts the graph of $f$ twice. Is $f$ a function or not?

Answer 1

Since, the vertical line through $x=6$ cuts the graph of $f$ twice.

That means vertical line test for functions does not holds.

It means that we will have two values of y corresponding to x=6.

Hence the uniqueness of image of $x=6$ does not holds .

So, $f$ is not a function