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# Recognizing functions from verbal description

## Video transcript

The value of y is always 3 more than twice x. So we can say that y is equal to 3 more than twice x. So it's 3 plus 2x 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 this function, you must get exactly one y. So if you input an x you must get exactly one y value. If you got two values, then 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 0, y is 3. If x is 1, y is 5. And so this is definitely a function of x. y is definitely a function of x.