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Understanding Step Functions 1073 Views
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- Functions / Analyze functions using different representations
- Functions / Analyze functions using different representations
- Functions / Analyze functions using different representations
- Functions / Analyze functions using different representations
- Functions / Analyze functions using different representations
Transcript
- 00:03
Understanding step functions a la shmoop [Woman running up steps]
- 00:06
you think you can stand on one foot for longer than your friend Derek, Derek thinks
- 00:12
he can go longer so you make it interesting Derek tells you that for
- 00:16
every two seconds you stand on one foot longer than him
- 00:19
he'll give you a starburst but if you cry uncle poor Derek you have to bake him
Full Transcript
- 00:24
a cake seems little lopsided sort of like [Woman holding a plate with a cake slice]
- 00:26
someone standing on one foot good news Derek falls down after only 47 seconds [Derek falls to the floor]
- 00:31
now you have to stand on one foot for at least two more seconds to earn anything
- 00:35
four seconds to earn two starbursts and so on well how can you figure out how
- 00:40
many starbursts you'll earn if you stay on your foot for an additional 15
- 00:44
seconds about 45 seconds two and a half hours
- 00:47
well we can't plot a line with a slope because the number doesn't go up
- 00:50
constantly for instance you stand 2.1 seconds
- 00:54
longer than Derek or you stand 3.9 seconds longer than Derek you'll still
- 00:58
get only one starburst, Derek doesn't have a sharp enough knife to cut the candies in
- 01:03
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]
- 01:08
do know how to plot points and that's all we need
- 01:10
so we graph this type situation using how you guess it step functions a type
- 01:16
of piecewise function but each of the functions within it will consist of only
- 01:21
constants making horizontal line, it's like a staircase, clever see those open
- 01:28
circles those correspond to the less than or greater than symbols in the
- 01:31
function well f of x equals 1 when x equals anything between 2 & 4 since the
- 01:37
function uses the less than or equal to next to the 2, 2 is included in this
- 01:43
function well unfortunately since the function uses the less than symbol with [Person points to less than symbol of piecewise function]
- 01:48
the 4.. F of 4 doesn't equal two starbursts it actually equals three and
- 01:53
the next horizontal line segment 4 is included with the less than or equal
- 01:58
to sign....As soon as you've passed that four second mark you
- 02:03
immediately move up the chain of command and get three starbursts notice there [3 starbursts appear on graph of step function]
- 02:08
wasn't a transition time when you got two and a half starbursts you just
- 02:11
jumped or should we say stepped straight to the next whole number all right well
- 02:16
this is why step functions come in handy the graph is still a function because [Hand catches step function]
- 02:20
every x value corresponds to only one y value see that? wow going on 25 minutes
- 02:25
we're impressed however you'd better call it quits and take a bathroom break [Woman and Derek standing on one leg]
- 02:28
soon or else you'll be gone to sharing something juicy...
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