How are my answers to these translations of the equations wrong ?

1. Reflect in the y-axis:

$y = \log x$ becomes $y = \log(-x)$



2. Translate by (-4,5)

$y = \log(-x)$ becomes $y-5 = \log(-(x+4))$

Why does $y = \log(-x)$ become $y-5 = \log(-(x+4))$ ? That would suggest that you perform the translation before you do the reflection. Yet, the question wants the reflection before the translation, so why is 2. not $y = log(-x + 4) + 5$ ?

It does not suggest that we do translation before the reflection.

We have already done the reflection.

If we are to do translation before the reflection, then the order would be:

1. Translation by (-4,5) -- this means replace y with y-5 and x with x+4.

$y = \log x$ becomes $y-5 = \log(x+4)$



2. Reflection in the y-axis -- this means replace x with -x

$-5 = \log(x+4)$ becomes $y-5 = \log(-x+4)$