why is this the answer? (1 Viewer)

anonymoushehe

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also, is the answer to this wrong, shouldnt it be C? cause if dilation was first then it would be f(x/3) then with translation it would be f[(x+2)/3]? Screenshot 2025-07-10 at 9.40.36 am.png
 

waltssillyhat

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also, is the answer to this wrong, shouldnt it be C? cause if dilation was first then it would be f(x/3) then with translation it would be f[(x+2)/3]? View attachment 48236
shouldn't the answer be a because in the question it says that the translation to the left by 2 units comes first before the horizontal dilation?
 
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waltssillyhat

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if it was the translation first you would get f(x+2) = g(x). Then sub in x/3, g(x/3) = f[(x/3) + 2]?
i think if the translation came first you would have x+2, and then you would apply the dilation to the entire graph thus far which is f(x+2), so it would be (x+2)/3. horizontal dilations and translations don't commute, so the order matters
 
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yourlocaliga

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wouldnt this depend on what function f(x) is? so the explaination isnt necessarily always right?View attachment 48235
i think the explanation is generally correct bc they specify the area as being halved so i cant really think of an example where it wouldnt be the case, but like the question doesnt specify and if it specified the evaluation of the integral then it would definitely depend on the function
 

liamkk112

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wouldnt this depend on what function f(x) is? so the explaination isnt necessarily always right?View attachment 48235
easy to do with u sub (not 2u technique though i think)

u = 2(x-3)
du = 2dx or du/2 = dx
x=6, u=6; x=4,u=2
then the integral becomes

so the answer is B.
not sure about their reasoning for it though
 

ros545

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Hi, does anyone, by any chance have Cambridge Year 12 Maths Ext 1 Chapter 4 and 10 worked solutions they could please possibly send? Thanks
 

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