Carolyn C. Wheater - Easy Pre-Calculus Step-by-Step: Master High-Frequency Concepts and Skills—Fast!

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Easy Pre-Calculus Step-by-Step is an interactive approach to the mathematics necessary for pre-calculus.

It contains completely detailed, step-by-step instructions for the skills and concepts that are the foundation for advanced mathematics. Moreover, it features guiding principles, cautions against common errors, and offers other helpful advice as pop-ups in the margins. The book leads you from basic algebra to a clear understanding of functions, explores fundamental trigonometry, and introduces you to the notion of limits. Concepts are broken into basic components to provide ample practice of fundamental skills. Pre-Calculus, as its name implies, is meant to prepare you for calculus, but what does that mean? To succeed in calculus, or any advanced mathematics, you will need strong algebraic skills as well as a clear understanding of functions in general and the many different types of functions specifically: polynomial, rational, exponential, logarithmic, and more. You will want to build skill in graphing quickly by means of transformations, and youll explore the polar coordinate system.

From the construction of the trigonometric ratios in right triangles to the definition of the trigonometric functions in the unit circle, you will extend your knowledge of relationships and how to apply them. You may even investigate sequences and series and peek into the future by exploring limits. Pre-Calculus may seem like too much to master, and the wide variety of topics may feel difficult to organize. With this step-by-step system, success will come. Learning pre-calculus, as with any mathematics, requires lots of practice. It requires courage to admit what you do not know, willingness to work on the problem, and a calm, orderly attempt to use what you do know.

Most of all, it requires a true confidence in yourself and in the fact that with practice and persistence, you will be able to say, I can do this! In addition to the step-by-step explanations and sample problems, this book presents a variety of exercises to let you assess your understanding. After working a set of exercises, use the solutions in the Answer Key to check your progress. We sincerely hope Easy Pre-Calculus Step-by-Step will help you acquire the competence and the confidence you need to succeed in pre-calculus, calculus, and all your mathematical undertakings.

A great deal of work in pre-calculus is centered on functions and their graphs. While the use of the graphing calculator has made it possible to explore many more, and many more complicated, functions than in the past, the ability to sketch the graph of a function by hand quickly is still an essential skill. Your first introduction to graphing was linear functions, and they will always be important. Many of the skills you developed with linear graphs will carry over to other functions. Recognizing the linear equations that dont behave in a typical fashion will save you time. Horizontal lines, because they have a zero slope, have an equation of the form y = c, where c is some constant. Vertical lines are the real oddity. They are not functions, and their equations dont fit the y = mx + b standard.

The equation of a vertical line is x = c, where c is a constant.

While constructing a table of values is always available as a graphing method, it is time consuming, and linear equations in particular allow for quick sketching methods. Slope-intercept. If the equation is in slope-intercept, or y = mx + b form, or can easily be converted to that form, plot the y-intercept (0, b), and then count the slope to locate other points on the line. Connect the points to create the line.