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We covered some foundational concepts, including domain and range, particularly when applied to rational functions. From these concepts, we touched on domain restrictions involving discontinuities, such as asymptotes and holes, then moved toward reviewing the definition of rational functions (including polynomial functions, in their abstract form), along with example problems, segueing into techniques for finding vertical, horizontal, and oblique (or slant) asymptotes. Finally, we looked at the fundamental theorem of algebra, and its better known form, "the n zeroes theorem." I also had the student do a practice problem that involved factoring using complex conjugates and long division. The student seemed to have a very positive disposition toward my exposition of the material, and his conceptual understanding of the material was solid. I encouraged the student to experiment with his calculator more, both to see what kinds of things it's capable of and take the opportunity to explore some of the more advanced mathematical concepts that it provides access to. Furthermore, I wanted to get the student in the habit of using his technological tools to check his work and do better error analysis to help identify his own mistakes.

Today we covered: How to translate from logarithmic form to exponential form and reverse; How to solve equations written in logarithmic or exponential form; and How to simplify rational expressions by finding common factors, factoring trinomials involved with multiplication and division. The student needs more practice with logarithms in fraction form as well as powers of a base. With factoring, more time must be spent with factoring binomials and trinomials. She appears to be getting a better grasp of the material.

We finished his geometry review packet. We also finished his homework on circles. He spent some extra time going through slope formula, distance formula, and midpoint.

The student and I went over concepts and problems in permutations and combinations. He grasped the concepts really quickly. He was very positive and eager to go over the material. I will send him a short practice problem set for our next session.

We had an organizational session for the new year, discussing the student's hours and math and science subjects. He will be taking algebra as his math class and biology as his science. I will be helping him with both.

Firstly, don't worry too much about your ability using the graphing calculator. Make sure to get used to using it in case the instructor asks you to use it during a problem online, but past that point I think you should concern yourself more with the mathematical concepts than a calculator. You have plenty of practice problems to work online, and I know you need to pass a certain amount of points soon, so if you need help with a problem, you can always email me a question you have. The biggest problem for students is typically the transition between the visual part, including graphs, and the algebraic part, including multiplying or adding functions. It seems you're having more of a problem with regard to the visual part. If you get used to the graphing calculator, if you so want to I would suggest making up different functions yourself and graphing them on it. This way, you will be able to see how different functions look. For instance, if you graph something like f(x) = x^3 + 4x - 2 and then graph f(x) = -(x^3 + 4x - 2), you should notice why the graph changed simply because you placed a negative sign in front of it. Graph functions and make small changes like these to them and you will notice a pattern among them. And don't forget to refer to the bullet points I made on what we went over. I'm looking forward to helping you next week.