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C1 question

This for C1 FOR THE EDEXCEL BOARD

I get how they got 1/2x - but then i dont know how to sketch it. and why are they showing 1/2 x 1/x

How would u sketch it?

tHANKS

Reply 1

StephenP91

Shame I can't see the question.

Reply 2

ztibor

Original post by jayseanfan

This for C1 FOR THE EDEXCEL BOARD

I get how they got 1/2x - but then i dont know how to sketch it. and why are they showing 1/2 x 1/x

How would u sketch it?

tHANKS

THe f(ax) transformation means streching f(x) perpendicularly on the y in
ratio of 1/a.
THe fix point is on y where the curve meets the y.
Every other point (f.e. with coordinates of x,y) of curve will be in 1/a *x distance
from y, so the coordinates will be (1/a)*x, y.
In special cases f(ax) can be written in form of b*f(x), which is another transformation.
bf(x) means streching f(x) in ratio of b perpendicularly on the axis x.
In your example 1/(2x) means pressing 1/x to 1/2 perpendicularly on y
or in (1/2)*(1/x) form pressing to 1/2 perpendicularly on the x, and
this two transformations are the same because 1/x is symmetric on line y=x

Reply 3

jayseanfan

Should i just learn which one goes above and which one goes beneath ?

Reply 4

ttoby

Original post by jayseanfan

Should i just learn which one goes above and which one goes beneath ?

You should be able to answer this question using the rules for what the transformations f(2x) etc do. If you're not sure how this affects the shape of the graphs then pick a few points and apply the transformation to them (in rough) to get an idea.

For example, for x=3, f(3)=1/3 and f(2*3)=f(6)=1/6
for x=1/3, f(1/3)=3 and f(2*1/3)=f(2/3)=3/2. You can start to see a pattern emerging and it should be clear that the transformed graph is sitting halfway between the original graph and the x axis, for x>0. You can then check a few points for x<0 to see where the graph lies there.

But since this method is fairly time consuming and doesn't get you marks, only use it if you're really stuck on how the transformed graph should look or if you have time at the end to go back and check your work.

I'd advise against just remembering which lines go above which because you might forget and get it wrong or there might be a similar question where the lines don't end up that way round.

Reply 5

Thrug

When the function is x it is 1 divided by x. So when the function is 2x it is 1 divided by 2x. You either have learnt the rule for this type of graph and no exactly what it does. Or, if not, put in values of (0.5, 1) and (1, 0.5) and you'll see the curve is closer to the axes.

f(x) = \frac {1}{x}

f(2x) = \frac {1}{2x}

(edited 13 years ago)

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