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# Does a vertical line represent a function?

Video transcript

In the following graph,
is y a function of x? So in order for y to
be a function of x, for any x that you input into
the function, any x for which the function is defined. So let's say we have
y is equal to f of x. So we have our little
function machine. It should spit out
exactly one value of y. If it spits out multiple values
of y, we don't know what f of x is going to be equal to. It could be equal to any of
those possible values for y. So let's see if, for this
graph, whether for a given x it spits out exactly one y. Well, the function
seems to be only defined so the domain of this function
is x is equal to negative 2. That's the only place where
we have a definition for it. And if we try to
input negative 2 into this little black
box, what do we get? Do we get exactly one thing? No. If we put in negative 2
here, we could get anything. The point negative 2,
9 is on this relation. Negative 2, 8 is
on this relation. Negative 2, 7; negative 2,
7.5; negative 2, 3.14159-- they're all on these. So if you put a negative 2 into
this relation, essentially, you actually get an
infinite set of values. It could be 9. It could be 3.14. It could be 8. It could be negative 8. You get an infinite
number of results. So since it does not
map to exactly one output of this function,
in the following graph, y is not a function of x.