CLEP College Mathematics: Functions

Functions are often described as a machine in a box that is open on two ends. You put something into one end of the box, it gets changed inside the box, and then the result pops out the other end. The ‘function’ is the machine inside the box and it is defined by what it does to whatever you put into it. This is a free online course that introduces you to special as well as polynomial functions. It outlines examples of polynomial functions and how to identify their degrees, for example, if each element of a matrix A is a polynomial in x and if |A| vanishes for x = a, then (x - a) is a factor of | A |. In this course, you will learn about two important theorems that are useful in searching for the roots of polynomial equations. The material also differentiates between the remainder theorem and factor theorem.

A relation between two sets is a collection of ordered pairs containing one object from each set. A function is a type of relation. But, a relation needs to have the object x in the first set to be related to more than one object in the second set. In this course, you will learn about the properties of relations and functions. It explains the arithmetic operations of addition, subtraction, multiplication and division. See how to prove that functions are Inverses. The material explains how to solve constants and identify functions using examples. Learn the difference between constant functions and identity functions. An absolute value function is a function that contains an algebraic expression within absolute value symbols. This course teaches you the geometric definition of the absolute value function and how to solve absolute values. Study the difference between linear functions and linear equations.

Finally, the greatest integer function is one that takes an input and gives an output that is the greatest integer that is less than or equal to the input. Master how to graph and solve greater integer functions. You will learn about exponential growth and exponential depreciation. See how to plot a graph of quadratic functions. This course also introduces you to graphical transformations. You will discover the properties preserved in all translations, reflections and rotations. The rotation of isometry will be discussed. This course will be of significant interest to those taking College-Level Examination Program (CLEP) math courses or who need a refresher in functions.