why is this the answer? (1 Viewer)

[anonymoushehe]

wouldnt this depend on what function f(x) is? so the explaination isnt necessarily always right?

 

[anonymoushehe]

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]?

 

[waltssillyhat]

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?

 

[anonymoushehe]

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

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]?

 

[waltssillyhat]

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

 

[anonymoushehe]

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

but the textbook says this:

 

[waltssillyhat]

but the textbook says this: View attachment 48237

oh yes my bad if the translation was first it should be x/3 + 2, so i think the answer should be c

 

[yourlocaliga]

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

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 sketching

 

[yourlocaliga]

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