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transformation question - is the answer wrong (1 Viewer)

anonymoushehe

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i got A but answer says D? if f(x) = ln x, shift left pi units should be f(x+pi) = ln (x+pi) = g(x), then dilation; g(1/3 x) = ln (1/3 x +pi) am i missing smth or
 

Gods_Spear

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i got A but answer says D? if f(x) = ln x, shift left pi units should be f(x+pi) = ln (x+pi) = g(x), then dilation; g(1/3 x) = ln (1/3 x +pi) am i missing smth or
I dunno I cant disagree with math gpt but in my mind this is d. You are missing somthing, with a horizontal dilation is gotta be outside the brackets as its dilating the whole x component (ie ln1/3(x + pi)) which can be distributed through the function to give D
 

tywebb

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I dunno I cant disagree with math gpt but in my mind this is d. You are missing somthing, with a horizontal dilation is gotta be outside the brackets as its dilating the whole x component (ie ln1/3(x + pi)) which can be distributed through the function to give D
it would be D if it were the other way around

like this

dilate horizontally by factor 3 first, so replace x with x/3, then it is y=ln(x/3)

THEN translate left by π, so replace x with x+π and it is y=ln((x+π)/3)

i sometimes disagree with mathgpt but in this case it is correct
 
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tywebb

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another way to understand this is the position of the asymptote

q.png

so for y=lnx asymptote is x=0

translate to left by π and asymptote is x=-π

then dilate horizontally by factor 3 and asymptote is x=-3π and the only one with that asymptote is A
 

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