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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?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
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]?The answer is a because in the question it says that the translation to the left by 2 units comes first before the horizontal dilation
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 mattersif 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]?
oh yes my bad if the translation was first it should be x/3 + 2, so i think the answer should be cbut the textbook says this: View attachment 48237
im pre sure A is the correct answer, bc they specify the order the transformations are applied in so you disregard the 'proper' order as u would apply when sketchingalso, 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
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 functionwouldnt this depend on what function f(x) is? so the explaination isnt necessarily always right?View attachment 48235