$y = \ln(4 - x) $
This graph has two operations applied to the $\ln x$ graph - a reflection and a translation.
If you reflect the graph in the $y$-axis first, and then shift the graph 4 units to the left you get an incorrect answer. The result is that the graph cuts the $x$-axis at $(-5, 0)$
BUT
If you shift the graph $4$ units to the left first, and then reflect the graph in the $y$-axis you get the correct answer. The result is that the graph now cuts the $x$-axis at $(3, 0)$ and the $y$-axis at $(0, ln4)$
Why is that? And is there an order as to which operation you must do first? Can someone please explain in simple terms as I do not understand why this is the case.
It's true that the last option is correct, what I want to show why they're different. This image, I think describes very well what's happening.
The blue lines signify the translation, the red lines signify the reflection over the y-axis. The lower blue points are the correct method, the upper green ones are the incorrect one.