Precalculus I (saylor.org)

Precalculus I is designed to prepare you for Precalculus II, Calculus, Physics, and higher math and science courses. In this course, the main focus is on five types of functions: linear, polynomial, rational, exponential, and logarithmic. In accompaniment with these functions, you will learn how to solve equations and inequalities, graph, find domains and ranges, combine functions, and solve a multitude of real-world applications.

In this course, you will not only be learning new algebraic techniques that are necessary for other math and science courses, but you will be learning to become a critical thinker. You will be able to determine what is the best approach to take such as numerical, graphical, or algebraic to solve a problem given particular information. Then you will investigate and solve the problem, interpret the answer, and determine if it is reasonable.

A few examples of applications in this course are determining compound interest, growth of bacteria, decay of a radioactive substance, and the maximum height of a rocket. You will also use a graphing calculator to model a data set and find the function of best-fit and then interpolate or extrapolate from that function.

Upon successful completion of this course, you will be able to:

- define the concept of function and determine the domain, range, inverse, and symmetries of functions;

- graph linear, absolute value, root, piecewise, polynomial, rational, exponential, and logarithmic functions and circles;

- identify the properties of polynomial and rational functions such as degree, maximum number of zeros, maximum number of turns, multiplicity of zeros, vertical asymptotes, horizontal asymptotes, and long-run behavior;

- compute the equations of linear, polynomial, rational, exponential, and logarithmic functions analytically given appropriate data;

- estimate solutions to and solve equations involving linear, absolute value, root, polynomial, rational, exponential, and logarithmic functions;

- solve inequalities involving linear, absolute value, and polynomial functions;

- utilize multiple approaches to describe functions such as verbally, algebraically, in tabular form, or graphically;

- solve and analyze application problems such as optimization or growth/decay, using the appropriate functions, and evaluate the reasonableness of the solution; and

- utilize technology to model linear, polynomial, exponential, and logarithmic data and interpret the results.