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#1 2006-01-24 01:43:29

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Scaling y=1/x

I have a question here that asks to explain the transformations and sketch the graph of
y=4/x
I know that on a graph of y=x² you can put y=x²+z and the curve will be moved along the y axis by z.  y = (x+z)² will move it along the x axis by z (but with a reversed sign).  Similarly y=2x² will double each y co-ordinate; How would I write it so that each x co-ord is doubled?

Also, back to my original question on the curve of y = 1/x, if y = -1/x rotates the curve in the x-axis, why is y = 4/x supposedly scaling in the y-direction?

Last edited by rickyoswaldiow (2006-01-24 01:47:33)


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#2 2006-01-24 02:16:29

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Scaling y=1/x

To enlarge the x co-ordinates of a function f(x), you need to change the function to f(ax), where 1/a is the amount that you want to enlarge it by.

So, to multiply all the x co-ordinates in y=x:sup2 by 2, you would have to change it to y=(x/2):sup2 = x:sup2/4.

And changing y = 1/x does scale it in the y direction, it just happens to scale in in the x direction as well because of symmetry.


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#3 2006-01-25 04:53:50

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: Scaling y=1/x

so y=2x² doubles each y co-ord and since y=1/2x² halfs each, that has the same effect as doubling each x co-ord?
With a curve of y=1/x, it gets scaled in both directions when the integer(1) there changes?


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#4 2006-01-26 10:51:52

God
Member
Registered: 2005-08-25
Posts: 59

Re: Scaling y=1/x

Picture y = -1/x as scaling the curve by a scale factor of -1.
The fact that you can also rotate the curve to get -1/x is a sidenote.

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#5 2006-01-26 16:36:43

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: Scaling y=1/x

y = -1/x rotates the curve in the x-axis
and
y = 4/x scales in the y-direction
are the "correct" answers shown in my a-level book. I don't see why they switch between y and x axis?


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