transformation question - is the answer wrong (1 Viewer)

[anonymoushehe]

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

 

[tywebb]

u are right

i put into mathgpt.org and it make solution


so A

 

[Gods_Spear]

View attachment 45750
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]

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

 

[tywebb]

another way to understand this is the position of the asymptote



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