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Introduction to linear functions

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what is a function before we talk about
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what a function is let's talk about
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juicers if I have a juicer and let's say
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I want to make orange juice all I have
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to do is put an orange in the juicer and
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out will come orange juice anytime I put
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an orange in the juicer it'll make
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orange juice for me my input would be
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that orange into the juicer and my
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output is the juice that comes out of
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the juicer notice that if I were to put
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grapes into the juicer I couldn't expect
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to get orange juice out of the juicer
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I'll get grape juice and if I put an
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apple in the juicer I'll get apple juice
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so for each type of fruit I put in the
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juicer I'll get that same type of juice
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out this is kind of like a function f of
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X equals 2x plus 1 is a good example of
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a function and you can think of f of X
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as a machine kind of like a juicer but
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instead of putting fruit in this machine
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we're going to put numbers and for each
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number we put into this machine we can
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expect to get one number out of the
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machine so for instance if i take the
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number three and i put it in this
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function this machine I can expect to
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get one number out and that number we
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can get by plugging in 3 into our
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function here's what we mean by that f
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of 3 is going to be 2 times so we have
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an X here we're going to replace it with
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a 3 so we have 2 times 3 plus 1 and that
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equals 6 plus 1 which is seven so when I
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put 3 into this function I can expect to
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get 7 out of it anytime I put 3 into
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this function I'll get 7 out in fact for
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any number that I put into this function
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there's only one number that will come
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of the function that's the definition of
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a function here's one more example of a
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function f of X equals 2 times X plus 3
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now we won't actually draw out a picture
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of a machine every time we want to
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evaluate a function at a given number
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but we can keep that picture in your
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mind to understand what's going on here
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let's evaluate F of 4 for practice so f
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of 4 equals 2 now we're going to replace
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X with 4 plus 3 and then we go then we
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just need to calculate what this is so
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we have 2 times 4 plus 3 which is seven
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and that leaves us with 14 so we know
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that F of 4 equals 14
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Short url:   https://clilstore.eu/cs/4917