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Graphing A PIECEWISE Function
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Feb 20, 2025
This is from a tutoring session I had a couple of days ago. I was showing my tutee how to graph PIECEWISE functions If you need help in math, be sure to check out http://tayibs.com/get-math-help/
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0:00
okay the goal is to graph this piecewise
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function now a piecewise function
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the name is self-explanatory f of X is
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equal to X if X is greater than or equal
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to 0 here and f of X is negative x if X
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is less than 0 so if you want to graph
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this function you have to respect the
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fact that this function is defined over
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one particular interval which is the
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numbers have to be between zero and
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positive infinity right so they can't be
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negative or any now yeah whoo graphic
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and then this one so basically what you
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do first is this you write the function
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f of X right and is equal to is a
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piecewise function so we have to have
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this X if X is greater than or equal to
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zero and negative x if X is less than
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zero so we take them one by one so the
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first thing the first step is this we're
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gonna graph this one okay so that means
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f of X is equal to X if X is greater
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than zero right so we make it a probe
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values and we're gonna take some random
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numbers for X and I'm finding that cost
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running so choose now when you want to
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choose those numbers it's better to
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start with no no no zero zero because
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what zeros is there's more than or equal
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to zero is included
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what is this thing indicated when is the
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line underneath da is equal to equal to
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seven zero can be included so that I
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mean if you graph the function it's
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gonna be a dot and not a certain
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occasion
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exactly so arrest to zero and what else
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another one we only need two point one
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right so when X is zero f of X will be
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what I'm gonna access so you plug it in
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here write f of X will be sure all right
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and then when X is one that's a big gray
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all you plug it in here when X when X is
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one you plug it in here
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right f of X will be wet if you replace
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X by one what would we have effects you
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rather think too much negative no
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locally if I plug-in I'm plugging in
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here so if X is one f of X will be 1 1 1
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that's it that that's what you're doing
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you just plug it in the values so you
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just go okay now we have that so let's
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go step by step now the next step is
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this we're gonna graph the second one
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right f of X is equal to negative x if X
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is strictly less than 0 we're gonna make
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a table again okay X and f of X and
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we're gonna plug in our values here so 0
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can't be in there cuz it needs to be
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great we go we still burning you put it
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in but when you watch a circle to
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indicate that zeros not included so it's
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better to start with zero gain for when
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x is 0 it will be 0 right
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and when X is pick another point no look
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at the interval no where are you where
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are you on your number line X is less
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than 0 or was negative negative 1
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negative 1 so when X is negative 1 F
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will be what no look negative negative 1
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so that becomes 2 negatives become
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positive whatever we want one okay now
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you have your two points you know you
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can grab your function right so let's
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draw a number line we're gonna draw a
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number line and if we're gonna take this
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and I'm going to send you this so in
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case you forget you can go back and
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watch
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Oh every day okay now let's do that okay
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so that strike the first function when X
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is zero right f of X is zero when X is
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one but we're gonna make a circle right
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yeah afterwards
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don't be graphing this one all right cuz
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he was included so we know we're gonna
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shop yet when X is zero f of X is easier
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when X is 1 is 1 right positive 1 no
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this is this one we're graphing this oh
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yeah so it goes this way right it just
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goes up not the other one
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but because my teacher she be making us
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do like a lot of you cannot just when X
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is 2 how many do you usually freeze good
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okay so when X is 2 f flex will be wet -
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right so 1 1 2 2 so that good yeah so
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now let's do this one let's add another
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way
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negative 2 right will be what - so we
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started when x is 0 this is 0 right we
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put a circle yeah
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when X is negative 1 f of X is gonna be
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right here right when X is negative 2
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it's 2
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so right here somewhere here right so
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the function is going like this
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absolutely absolutely right this is it
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for this one