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If f(x) = x + 1
If j(x) = f(x-1)
What is happening here?
igloo myrtilles fourmis
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f(x-1) = (x-1)+1 = x
j(x) = x
?
The Beginning Of All Things To End.
The End Of All Things To Come.
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simple, j(x) = f(x-1), this means that whatever you input for j, the value of j(x) is equal to the value of inputing x-1 into f.
if you substitute, you will find that j(x) = f(x-1) = (x-1) + 1 = x.
whats confusing about these is that x is just a generic value that represents the input to the function. so when we say
f(x) = x + 1 and
j(x) = f(x-1)
the x's in these two function definitions have nothing to do with eachother.
A logarithm is just a misspelled algorithm.
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Thanks a bunch L & M !
igloo myrtilles fourmis
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I believe the question is looking for a short and concise answer, which would be "shift to the right by 1".
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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Whoa!! That's awesome. Neat how shifting this graph to right is done with x - 1 replacing x.
Makes sense. And also for this specific case, shifting the graph down by 1 does the same thing,
or down and right at a -45 degree angle for about .707 . But actually then the infinity case
would be in a different place by a tad, but who's counting at infinity. But the line has no ends, so
the infinity case doesn't really have endpoints that move I guess.
igloo myrtilles fourmis
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What do you mean by "infinity case"?
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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I mean at the end of the diagonal line, but it has no end, so maybe there is no infinite case.
Like if you shift the y = x + 1 line into the y = x line position, there are infinitely many
ways you could do it. You could go 1 unit to the right as you have made clear.
I love that way, as it works for all functions in the example about j(x) above.
However, you could alternatively move the top line (y = x + 1) down to the
lower line (y = x) by moving the whole line at a 44 degree angle for approximately
40.51629119 units. This I got with a tiny bit of trig.
igloo myrtilles fourmis
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There may be infinitely ways to do it, but they all end up being the same line. For example, I could just as easily move it 55 units to the left, then 56 units to the right. This is basically all you're doing.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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Yes, I do think you are right.
What I was trying to do was
express the feeling I had that
if the line was not homogeneous,
then it would be more than
just a plain old reference line with
zero width and no character or
details except to make a relationship
between y and x. But it was
simply a thought I hoped would
go somewhere, but I still strive
for things I cannot comprehend.
igloo myrtilles fourmis
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