transformation of graphs Watch

Alen.m
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Hi Guys,
the question on the attachment seems like a stretch in y direction but the answer is a stretch by a factor of 1/10 in x direction. can anyone explain that to me please? thanks
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nerak99
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It is all from manipulation of logs. 1 = log 10 and hence we have log 10 + 2 log x = log 10 + log x^2 = log (10 times x^2.)

Since our original function is 2log x = log (x^2). This is of the form of a transform f(x) to f(10x) and so is a stretch by a SF 1/10 in the x-direction
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Alen.m
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(Original post by nerak99)
It is all from manipulation of logs. 1 = log 10 and hence we have log 10 + 2 log x = log 10 + log x^2 = log (10 times x^2.)

Since our original function is 2log x = log (x^2). This is of the form of a transform f(x) to f(10x) and so is a stretch by a SF 1/10 in the x-direction
so in this kind of question you have to play around with the second equation till you get the first one? can't it be stretch in positive y direction as the whole function has been added by 1?
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nerak99
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(Original post by Alen.m)
so in this kind of question you have to play around with the second equation till you get the first one? can't it be stretch in positive y direction as the whole function has been added by 1?
Not really as the case for transforming f(x) by a y stretch is kf(x) and a x stretch is f(kx). In a q like this you need to transform the function into a form like

kf(x) (y sf k)
f(kx) (x sf 1/k)
f(x) + k (translate y by amount k)
f(x+k) (translate x by amount -k)
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