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Understanding step functions a la shmoop [Woman running up steps]

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you think you can stand on one foot for longer than your friend Derek, Derek thinks

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he can go longer so you make it interesting Derek tells you that for

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every two seconds you stand on one foot longer than him

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he'll give you a starburst but if you cry uncle poor Derek you have to bake him

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a cake seems little lopsided sort of like [Woman holding a plate with a cake slice]

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someone standing on one foot good news Derek falls down after only 47 seconds [Derek falls to the floor]

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now you have to stand on one foot for at least two more seconds to earn anything

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four seconds to earn two starbursts and so on well how can you figure out how

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many starbursts you'll earn if you stay on your foot for an additional 15

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seconds about 45 seconds two and a half hours

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well we can't plot a line with a slope because the number doesn't go up

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constantly for instance you stand 2.1 seconds

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longer than Derek or you stand 3.9 seconds longer than Derek you'll still

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get only one starburst, Derek doesn't have a sharp enough knife to cut the candies in

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pieces so you can only receive a whole number amount of starbursts well but we [Derek holding a starburst while woman stands on one leg]

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do know how to plot points and that's all we need

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so we graph this type situation using how you guess it step functions a type

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of piecewise function but each of the functions within it will consist of only

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constants making horizontal line, it's like a staircase, clever see those open

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circles those correspond to the less than or greater than symbols in the

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function well f of x equals 1 when x equals anything between 2 & 4 since the

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function uses the less than or equal to next to the 2, 2 is included in this

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function well unfortunately since the function uses the less than symbol with [Person points to less than symbol of piecewise function]

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the 4.. F of 4 doesn't equal two starbursts it actually equals three and

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the next horizontal line segment 4 is included with the less than or equal

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to sign....As soon as you've passed that four second mark you

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immediately move up the chain of command and get three starbursts notice there [3 starbursts appear on graph of step function]

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wasn't a transition time when you got two and a half starbursts you just

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jumped or should we say stepped straight to the next whole number all right well

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this is why step functions come in handy the graph is still a function because [Hand catches step function]

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every x value corresponds to only one y value see that? wow going on 25 minutes

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we're impressed however you'd better call it quits and take a bathroom break [Woman and Derek standing on one leg]

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soon or else you'll be gone to sharing something juicy...

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