In this unit, you will learn important terminology and characteristics of linear equations, inequalities, and their graphs. Additionally, we will cover how to solve general linear equations in one variable, literal equations, and compound inequalities. You will also explore how to graph linear equations and inequalities in two variables on a coordinate plane, learn how to solve systems of two or three linear equations, and apply these skills to real-world applications. You may want to refer to this unit as you move through the course. For some, this material may be a repeat, and you will be able to move quickly. For others, it may have been a long time since you practiced the concepts in this unit, and taking the time to become fluent with solving and graphing equations and inequalities will pay off later in the course.
Completing this unit should take you approximately 4 hours.
The study of functions is one of the main focuses of this course. In this unit, we will introduce the definition of a function and the special notation used to write equations for functions of two variables. You may find some of the material is familiar if you have already learned about plotting points on the cartesian coordinate plane and writing equations of lines. You will be introduced to a toolkit of functions early in the unit that we will use throughout most of the course, so pay close attention to the characteristics and notation used to define them. You will practice defining important characteristics of functions such as the domain and range. You will practice graphing the many different types of functions that we will focus on throughout the course. Pay close attention to this unit, as it builds the foundation for the course. Enjoy your study of functions!
Completing this unit should take you approximately 3 hours.
In this unit, you will deepen your knowledge of functions by performing algebraic operations on functions and learning how to transform graphs of functions. You will continue to define important characteristics of functions, including domain and range, after performing algebraic operations or transformations on the graphs of functions. This is another fundamental unit, so pay close attention to what kinds of transformations can be performed on the graphs of functions and how they change the key characteristics of the function's equation, domain, and range. In later units, you will apply the same transformations to the toolkit functions you discovered in Unit 2.
Completing this unit should take you approximately 3 hours.
In this unit, you will explore linear functions in depth. Linear functions are a great place to start our in-depth exploration of functions because they are fairly straightforward to master, and many people have learned about them in past math courses. In our discovery of linear functions, we will work with tables, equations, graphs, and words to describe the behavior and key characteristics of linear functions. You will also learn about an important concept called the rate of change. One of the most important key characteristics of a linear function is its rate of change. If you continue on to study calculus, you will learn about the rate of change in depth. In addition to the rate of change, you will discover that some observable phenomena behave linearly. We can build a model using a linear function to represent their behavior and make predictions.
Completing this unit should take you approximately 2 hours.
Polynomial functions include quadratic functions, which may be familiar to you from past math courses. In this unit, we will continue the pattern of defining key characteristics of polynomial functions such as the domain and range using equations and graphs. In addition to quadratic functions, the family of polynomial functions includes functions with higher degree exponents. As the degree of a polynomial increases, the algebra required to define its key characteristics such as intercepts and inflection points becomes more and more complicated. You will learn techniques to describe the behaviors of polynomial functions that help us understand them without performing complex algebra.
Completing this unit should take you approximately 4 hours.
In this unit, you will apply what you have learned about functions to rational functions. Rational functions are based on the toolkit reciprocal functions and have many interesting characteristics. You will apply similar skills and techniques for defining intercepts and end behavior of polynomial functions to rational functions. By the end of this unit, you will be proficient in defining the local behavior and end behavior of a polynomial function and drawing the graph of a polynomial function given its characteristics.
Completing this unit should take you approximately 2 hours.
Welcome to the final unit on functions. In this unit, you will learn about exponential and logarithmic functions. Exponential functions are often used to model the behavior of populations and the growth of an investment or debt. You will learn the characteristics of an exponential function and become proficient at graphing them given key components. In addition to exponential functions, you will learn about the logarithmic function. The logarithmic function is the inverse of the exponential, and we will explore the relationship between the two.
Completing this unit should take you approximately 3 hours.
Now that you know all about exponential and logarithmic functions, you can learn how to solve equations that involve them. You will use the properties of logarithms and exponentials and the fact that they are inverses to solve equations. You will also explore some applied problems involving exponential and logarithmic equations. Finally, you will learn to fit exponential and logarithmic models to data.
Completing this unit should take you approximately 3 hours.
Systems of equations are handy when exploring the relationship between two or more things. For example, the profit a business makes is dependent on both the cost to produce goods or services and the money it brings in from selling those goods or services. We will introduce methods for solving systems and interpreting the solution when you find one. We will also introduce techniques for graphing systems of inequalties that include combinations of linear and quadratic equations. You will use the skills you have learned from working with linear and quadratic functions and from graphing and solving linear inequalities to master the topics in this unit.
Completing this unit should take you approximately 3 hours.
Conic sections are made by taking particular slices of a cone. The slices we will study include ellipses, hyperbolas, and parabolas. You will have studied parabolas in the context of functions previously in the course, but these parabolas are different because they are not functions. Read on to learn more!
Completing this unit should take you approximately 2 hours.
In this final unit, we will introduce the basics of defining, notating, and evaluating sequences and series. You will explore arithmetic sequences, geometric sequences, and series, and you will learn to distinguish between them.
Completing this unit should take you approximately 2 hours.
This study guide will help you get ready for the final exam. It discusses the key topics in each unit, walks through the learning outcomes, and lists important vocabulary. It is not meant to replace the course materials!
Please take a few minutes to give us feedback about this course. We appreciate your feedback, whether you completed the whole course or even just a few resources. Your feedback will help us make our courses better, and we use your feedback each time we make updates to our courses. If you come across any urgent problems, email contact@saylor.org.
Take this exam if you want to earn a free Course Completion Certificate.
To receive a free Course Completion Certificate, you will need to earn a grade of 70% or higher on this final exam. Your grade for the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again as many times as you want, with a 7-day waiting period between each attempt. Once you pass this final exam, you will be awarded a free Course Completion Certificate.
Take this exam if you want to earn college credit for this course. This course is eligible for college credit through Saylor Academy's Saylor Direct Credit Program.
The Saylor Direct Credit Final Exam requires a proctoring fee of $5. To pass this course and earn a Credly Badge and official transcript, you will need to earn a grade of 70% or higher on the Saylor Direct Credit Final Exam. Your grade for this exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again a maximum of 3 times, with a 14-day waiting period between each attempt.
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Once you pass this final exam, you will be awarded a Credly Badge and can request an official transcript.