About College Algebra
Real Numbers. This topic of College Algebra introduces the real number system in an informal and intuitive manner. First we define the following sets of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and the real numbers. Then we state and illustrate how to use the (axioms) properties of the real numbers. We follow this by detailing many more properties of the real numbers such as, cancellation properties, distance properties, and absolute value properties.
Exponents and Radicals. Usually, there are many ways to solve a problem in algebra. The more fluency you have with exponentials and radicals the more options you have in your procedure of simplifying algebraic expressions.
Graphs of Equations. Descarte's Cartesian coordinate system is defined and then it is shown how to make graphs of relations. Functions are then defined and it is explained how to determine if a set or ordered pairs defines a function or not. The vertical line test is detailed and functional evaluation is shown.
Definition of a Function. Descarte's Cartesian coordinate system is defined and then it is shown how to make graphs of relations. Functions are then defined and it is explained how to determine if a set or ordered pairs defines a function or not. The vertical line test is detailed and functional evaluation is shown.
Graphs of Functions. In this topic of College Algebra we show the graphs for the five basic functions: the square function, the abolute value function, the cube function, the square root function, and the cube root function. Translations are covered by shifting graphs vertically and horizontally. Basically, vertical shifts work the same as the given sign and horizontal shifts work opposite the given sign. Then reflections of these graphs are shown, as well as, examples with translations and reflections. Finally, vertical stretches and vertical shrinks are illustrated.
Quadratic Functions. Quadratic functions are polynomial functions of degree 2 and are usually studied after linear functions. The method of completing the square is detailed and it is shown that completing the square of the general quadratic equation leads to the quadratic formula. Graphing quadratic equations, including intervals of increasing and decreasing, vertex, line of symmetry, and maximium and minimium values are also illustrated.
Exponential Functions. Exponential functions are used throughout the sciences and are particular useful in business applications. For example, most banks in the world use the exponential function with simple and compound interest. In this topic of College Algebra we concentrate on decay and growth models, which are two different types of exponential functions, and we emphasize graphs and the properties exponential. We also show by example how to solve exponential equations. This topic explains simple interest and compound interest through a series of problems and examples.
Natural Exponential Function. In this topic we concentrate on compounding continuously and the annual percentage rate is also worked on. Attention is given to the problem of finding the doubling time for an investment.
About College Algebra
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/about-college-algebra.html
