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Identifying Dependent And Independent Variables In A Function
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Feb 20, 2025
I was helping my son who is a freshman in high school with identifying independent and dependent variables in a function. The identification is easy when the function is given in mathematical terms but gets harder when it’s an actual problem that has to be translated in mathematical terminology. The problems we worked on tonight were very simple and I hope this little tutorial helps
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okay now we're working on word problems
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and we have to find independent and
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dependent variables right okay let's
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read the problem gone reader even read
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it okay Hector Services is raising money
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by wrapping present in the mall the
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function FX equals 3x describes the
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amount of money in dollars the club
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would earn for wrapping X present they
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only have enough weapon paper to wrap a
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thousand presence and then the question
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is described a dependent variable for
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this problem so which one is dependent
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what depends on what is the question
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laughing paper for presents okay the
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dependent is the money right the money
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you get depends on how many presents you
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wrap right so the deep end it will be
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the money there ma correct yes let's
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write that down so the money I earn is
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the dependent on your number for the
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world 3 oh here you're here we're here
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no we're not doing that we're here this
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is the problem with red always asking
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for this way
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okay well let's finish this one okay all
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right now the next question is describe
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to do me and arrange for this problem
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using appropriate notation right so
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what's the domain the domain is in this
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case will be no the domain will not be
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the money the domain will be the maximum
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number of presence in you can write and
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the domain between 0 and 1000 so let's
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write that down
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good job and then if the rain hooby are
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between again zero and 8,000 times three
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sweetie right okay three times so let's
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write that now and that's it for this
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question you get it we start working
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with word problems that have to do with
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functions that have independent and
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dependent variables correct in this case
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we are talking about geometry and now we
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have the problem says the surface area
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of a cube can be found using the
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following formula a equals 6 s square
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where a represents the surface area of
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the cube and S stands for the length of
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one edge now your geometry teacher wants
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you to draw a cube that has a length of
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at least five inches correct and then
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the question is describe the independent
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variable for this problem okay so now we
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have the function this is the function a
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stands for the surface area and then
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since 6 XS squares that I start the
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actual um
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given our function there right now S
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stands for one of the edges okay so in
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this case s will be your dependent and
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independent variable and it's gonna be
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called the length of one of the H
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correct you got it because this is s is
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the length of one of the edges so as
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will be your independent variable cuz
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that changes right that's gonna change
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so s is going to be the independent ID
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we call ID and then now the next
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question is finally domain of this
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function now we have a little problem
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here there's telling us that it took on
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this cube has a length of at least five
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inches at least five inches is five
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inches or more right we don't have a
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limit at what we know that is at least
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five inches so that means our domain
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between five and infinity you got it
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yeah and now to find it the range we're
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gonna do the same thing we're gonna
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start at 5 inches we're gonna plug it in
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here
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correct so the rent would be six times
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ubi let's find six let's let me put it
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down here somewhere if you do six times
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five squared that's six times 25 plus
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six times twenty-five every six times
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five is thirty six down to 150 right
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double check it so it's gonna be the
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language between 150 and what infinity
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so that makes sense
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you get it yeah all right that's it