Math Is Fun Forum

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

changing input x

If f(x) = x + 1
If j(x) = f(x-1)
What is happening here?

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igloo myrtilles fourmis

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: changing input x

f(x-1) = (x-1)+1 = x
j(x) = x

?

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The Beginning Of All Things To End.
The End Of All Things To Come.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: changing input x

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.

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A logarithm is just a misspelled algorithm.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: changing input x

Thanks a bunch L & M !

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igloo myrtilles fourmis

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: changing input x

I believe the question is looking for a short and concise answer, which would be "shift to the right by 1".

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"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..."

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: changing input x

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.

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igloo myrtilles fourmis

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: changing input x

What do you mean by "infinity case"?

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"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..."

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: changing input x

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.

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igloo myrtilles fourmis

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: changing input x

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.

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"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..."

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: changing input x

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.

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igloo myrtilles fourmis