The point I would make (and that I think many experts in math education would make) is that engineers and mathematicians use functions as a core part of how they work with mathematical ideas
Yet in algebra we do this funny thing to students. We start them off of with equations (not functions) and get them to do this little procedural dance to solve for 'x'.
Then we throw them functions, which look an awfully lot like equations but are different in core ways. This is intellectually jolting, and high school curricula don't at all do a good job of explaining the difference. It is pretty easy to show (if you are around high school students) that this method leads to some pretty deep misunderstandings of mathematics.
Students are perfectly able to understand this level of math using functions and solution sets. The advantage is that this puts the focus of the math learning on modelling and thinking about the context.
I have seen this type of curriculum work... where functions are introduced near the beginning of Algebra 1. Equations aren't that important (once you learn to work with functions), I don't know why we insist on making them the focus of Algebra class.
In any case, in the Algebra Classes at the high school where I taught, in the middle of Algebra 2, the kids started working with functions after years of working with equations. They would come into my physics classes mathematically confused.
That is why I assume that I understand Hayley's homework. It looks awfully familiar to work that my students would be asked to do. And yes, the math teachers were trying to shift their focus into thinking about functions as "objects".
Students in Algebra 2 have to do function composition, where they can take f(g(x)) and give the answer... without ever solving for x. The point is to understand function composition.... which is a little difficult if you haven't really understood what functions are.