Add content regarding multiple transformations at a time in graphs (Pre Calculus)

Hello there.

I hope you are having a wonderful day.

I couldn't find any videos that covered how to apply multiple transformations to the equation of a graph.

For example, something that I am struggling to understand is if we have a graph called f(x), and then we stretch it horizontally by a factor of 1/2, and then translate it horizontally by four units, I do not understand why the new graph's equation is g(x) = f(2(x - 4)), with the translation being inside of the stretch, making it seem like it is being applied first, rather than the stretch being applied first.

In other words, how should we derive the equations of graphs after they have been stretched and translated in the same direction, and the logic behind it.

A video on replacements in the equations of graphs would also be greatly appreciated.

Thank you for your time.