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# Recognizing functions from verbal description

## Video transcript

the value of y is always three more than twice X so we can say that Y is equal to three more then twice X so three more than twice X so it's three plus two X is another way of saying this first sentence so is y a function of X so whenever you're asked whether something is a function of something else you're really just saying look for any input X does it map to exactly one y so if we say Y is a function of X in order for this to be a function for any X that you input into the function you must get exactly you must get exactly one y so if you input an X you must get exactly one y value if you got two values that it's no longer a function for any input you get exactly one y you could have two inputs that get to the same Y but you can't have one input that results in two different outputs you don't know what the function is valued at at that input now here it looks pretty clear that for any input you get exactly one output any input uniquely determines which Y it's not like if you put an X in here you're not sure what Y is going to be you know what Y is going to be if X is zero Y is three if X is one y is five and so this is definitely a function of X Y is definitely a function of X