CLEP College Algebra: Functions, Sequences and Series
This free online course examines functions and the basics of manipulating functions, sequences, as well as series.Publisher: ADU
CertificationView course modules
Algebra is one of the broad areas of mathematics, together with number theory, geometry, and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. This free online course analyzes some of the most important aspects of algebra. The course begins by introducing you to the basics of relations and the characteristics of functions.
Next, the course takes you through the test for symmetry and composition on functions. Symmetry can be useful in graphing an equation since it says that if we know one portion of the graph then we will also know the remaining portion of the graph as well. We use this fact when we are graphing parabolas to get an extra point of some of the graphs. Cartesian coordinates are the foundation of analytic geometry and provide enlightening geometric interpretations for many other branches of mathematics. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering, and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design, and other geometry-related data processing. This course outlines how to ploy points on the Cartesian coordinate system and some definitions of terms. You will also learn about how to graph a linear inequality.
In elementary algebra, the quadratic formula is a formula that provides the solution to a quadratic equation. The word "Quadratic" is derived from the word "Quad" which means square. In other words, a quadratic equation is an “equation of degree 2.” There are many scenarios where a quadratic equation is used, this course identifies some of these situations. You will learn about the different methods of solving quadratic equations with the aid of examples. Sequence and series are some of the most basic topics in Arithmetic. An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series is the sum of all elements. An arithmetic progression is one of the common examples of sequence and series. This course identifies the different types of sequences and series, as well as how to manipulate them. So, register for this course today and begin your next learning journey!Start Course Now
Introduction to Functions
Introduction to Functions - Learning Outcomes
Relations and Functions
Test for Symmetry
The Cartesian Coordinate System
Graphing a Linear Inequality
The Discriminant and Nature of Roots
Quadratic-Linear Systems of Equations
Introduction to Functions - Lesson Summary
Exponential and Logarithmic Functions
Exponential and Logarithmic Functions - Learning Outcomes
Graphing Polynomial Functions
Solving Logarithmic Equations
Graphical Transformations of Functions
Exponential and Logarithmic Functions - Lesson Summary
Sequences and Series
Sequences and Series - Learning Outcomes
Sequences and Series
The Binomial Theorem
Sequences and Series - Lesson Summary
Upon the successful completion of this course, you should be able to:
- Explain how to solve systems of equations and inequalities.
- Describe the properties of translations and dilations.
- Recall how to test a function for symmetry.
- Identify the symbol for sigma notation.
- Explain how to plot points on the coordinate plane.
- Describe how to change between exponential and logarithmic form.
- Discuss how to solve for binomial expansion with coefficients.
- List the formulas for finding the sums of sequences.
- Differentiate between geometric sequences and geometric series.
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