## Topics in## PRECALCULUS11. The formal rules of algebra 12. Rational and irrational numbers What is a rational number? Which numbers have rational square roots? The decimal representation of irrationals. What is a real number? 13. Functions What is a function? The domain and the range. The graph of a 15. Basic graphs The constant function. The identity function. 16. The vocabulary of polynomial functions Variables versus constants. The degree of a term and of a polynomial. The leading coefficient. The general form of a polynomial.17. The roots, or zeros, of a polynomial A 18. The slope of a straight line Definition of the slope. Positive and negative slope. 19. Linear functions: The equation of a straight line The equation of the first degree. The graph of a first degree equation: a straight line. 10. Quadratics: Polynomials of the second degree Quadratic equation: Solution by factoring. Solving a quadratic equation by 12. Synthetic division by The remainder theorem. 13. Roots of polynomials of degree greater than 2 The factor theorem. The fundamental theorem of algebra. The integer root theorem. Conjugate pairs. 14. Multiple roots. Point of inflection. Concave upward, concave downward. Reflection about the Symmetry with respect to the Definition of a translation. Singularities. The reciprocal function. Definition of inverses. Constructing the inverse. 20. Logarithms The system of common logarithms. 21. Logarithmic and exponential functions Inverse relations. 23. Factorials 24. Permutations and Combinations The Fundamental Principle of Counting. Pascal's triangle. A proof of the binomial theorem. |