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# Checking if a table represents a function

Video transcript

In the following table,
is y a function of x? In order for y to
be a function of x, for any x that we input into
our little function box-- so let's say this is
y as a function of x. It needs to spit out
only one value of y. If it spit out
multiple values of y, then it might be a
relationship, but it's not going to be a function. So this is a function. This is a function. If we had a situation where
if we input x into a box, it could be multiple
possible y's, then this is not a function. So let's think about this
table right over here. When x is equal to 1,
we get y is equal to 1. But when x is equal to 1
again, all of a sudden, y is equal to 2. So here we have a
situation where we input 1 into our little
relationship box, and when we input 1 into
our relationship box, we could get a 1, or
we could get a 2 for y. So this is definitely
not a function. For any input into
a function, it has to map to
exactly one output. Here it's mapping
to two outputs. So this is not a function.