What is the purpose of precalculus considering that most precalculus topics are covered in algebra 2 and trig and also in college algebra?
precalculus is basically bridging the gap between algebra, trigonometry and calculus, and finalizing the last few things you need to know before going into calculus. It is here where you have to focus on such things as the fundamental theory of algebra, function operations and function composition, even and odd functions, getting the roots of nth degree equations, z substitution techniques, function and matrix transformations, graphing functions (to the extent that they can be graphed without making use of its derivatives), getting rid of all your small basic math careless mistakes and habits, understanding different coordinate systems, conics, some discrete math concepts such as the difference between a domain, function, image; and any other processes and concepts involved in calculus that are in addition to limits, integral, derivatives, infinitesimals, riemann sums, and the fundamental theorem of calculus. I believe also that a goal in precalculus is to know the full extent and limitations of what you can do with the mathematics that comes before calculus.