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# Recognizing functions from verbal description

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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.