ShmoopTube

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Functions, a la Shmoop. Ever see something that is...dysfunctional?

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Like some families, for instance. Or a society with no rules.

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Now, picture the world without functions. Without functions, zebras would equal monkeys...

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...and 2 + 2 would equal bananas. Picture functions as the parent...

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... and variables as the children. Some variables are a little more independent

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than others. Functions love to tell variables what to do...

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...but not all variables follow the rules. Independent variables are the free thinkers.

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They can be anything, and they know it.

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A dependent variable is the kid that never moves out of the house.

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They don't really have a plan, and just go with the flow.

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They sit around, letting the function tell them what to be.

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So, if you have the function f(x) = 3x + 2... ...f(x) is the function, and 3x + 2 is the

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rule that needs to be followed. By the way, don't freak out about the weird

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f(x) thing. It's a little something we like to call "notation"...

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...and it's read either as, "f is a function of x" or "f of x".

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"x" is where you plug in the independent variable. Oh, and f(x) also equals the dependent variable

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y. Plugging in a free thinking independent variable,

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such as 2... ...we get f(2) = 3(2) + 2 = 6 + 2 = 8 = y.

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Getting the answer 8 depends on what you plug in for x.

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If the independent variable decides he wants to be the number 4...

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...we get f(4) = 3(4) + 2 = 12 + 2 = 14. You can plug any number into "x," and some

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other number will come out the other end. And there a lots of functions out there.

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We kind of hope that dependent variable doesn't get too adventurous...

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...or else we might be in trouble.

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