Topics inPRECALCULUSInternet Explorer 6 is the browser to view these pages, and Garamond is the font. 11. 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? Functional notation. A function of a function. The graph of a function. Coördinate pairs of a function. The height of the curve at x. 15. Basic graphs The constant function. The identity function. The absolute value function. A parabola. The square root function. The cubic function. 16. The vocabulary of polynomial functions Definition of a polynomial in x. 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 The polynomial equation. The roots of a polynomial. The x- and y-intercepts of a graph. The relationship between the roots and the x-intercepts. 18. The slope of a straight line Definition of the slope. Positive and negative slope. A straight line has only one 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. The slope-intercept form, and its proof. 10. Quadratics: Polynomials of the second degree Solving a quadratic equation by factoring. A double root. Quadratic inequalities. The sum and product of the roots. Solving a quadratic equation by completing the square. The quadratic formula. 12. Synthetic division by x − a 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 x-axis. Reflection about the y-axis. Reflection through the origin. Symmetry with respect to the y-axis. Symmetry with respect to the origin. Test for symmetry. Odd and even functions. Definition of a translation. The equation of a circle. Singularities. The reciprocal function. Horizontal and vertical asymptotes. ![]() Definition of inverses. Constructing the inverse. 20. Logarithms The system of common logarithms. The system of natural logarithms. The three laws of logarithms. 21. Logarithmic and exponential functions ![]() 22. Factorials 23. Permutations and Combinations The Fundamental Principle of Counting. Factorial representations. Pascal's triangle. A proof of the binomial theorem. ![]() ![]() TheMathPage depends on donations. |