Some suggestions for the first days of school:
There has to be a first day, so make the most of it. Take roll; make sure everyone is in the right place. Give out the textbooks. Explain about calculators and so on.
A word about reviewing at the beginning of the year: Don’t!
If you textbook’s first chapter is a review of pre-calculus, then assign the class to read this chapter. Tell the class that the next day your will answer any questions they have and, after that, for the rest of the year they should refer back to this chapter when they need more information on these topics.
Start day 2 with your first lesson on limits.
Plan to review material from Kindergarten thru pre-calculus when the topics come up during the year – and they will come up. In some cases, plan for them to come up. For instance, the year usually begins with the study of limits. In connection with limits you will be looking at lots of graphs: this is a perfect time to review the graphs of the parent functions, a lot of the terminology related to graphs, discontinuities, asymptotes, and even the values of the trigonometric functions of the special angles.
Months from now you will teach about the derivatives of inverse functions. That is when you review inverses. Review inverses now and you will have to do it later anyway.