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Video transcript

in the following graph is why 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 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's puts out multiple event 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 this 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 if we try to input negative 2 into this little this little black box what do we get do we get exactly one thing no we put a negative 2 here we could get anything negative 2 the point negative 2 9 is on is on this relation negative 2 8 is on this relation negative 2 7 negative 2 7 point 5 negative 2 3.14159 they're all on these so if you put a negative 2 into this relation you actually get you actually get 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 you it does not map to exactly one output of this function the following graph y in the following graph y is not a function of X