Algebra: Elementary to Advanced - Functions & Applications

Go to Course: https://www.coursera.org/learn/algebra-ii

Introduction

**Course Review: Algebra: Elementary to Advanced - Functions & Applications on Coursera** If you’re looking to build or refresh your understanding of algebra, particularly in the area of functions and their applications, the course "Algebra: Elementary to Advanced - Functions & Applications" on Coursera is an outstanding choice. This course caters to a wide array of learners, from those who are simply looking to solidify their foundational knowledge to those seeking to explore complex applications of functions in various fields. ### Course Overview The course dives deep into the world of functions, guiding students to not only understand fundamental concepts but also apply them in real-world scenarios. It begins with a detailed examination of what a function is, moving smoothly through essential types—linear and quadratic—before branching out into more complex functions. Throughout the course, students will learn valuable techniques for modeling data, solving problems, and analyzing different types of functions, ensuring that they are well-prepared for a variety of situations. ### Syllabus Breakdown **Module 1: Introduction to Functions** This module sets a solid foundation by introducing linear relationships. Students will learn about the characteristics of linear functions, exploring how they can model real-life scenarios where there is a consistent change in one variable concerning another. The transition to quadratic functions introduces the parabolic graph, deepening the participants' appreciation of algebraic relationships. **Module 2: Other Common Functions** Building on the knowledge from the first module, this segment focuses on constructing new functions through graph shifting techniques, encouraging students to visualize functions as they solve problems. This approach bolsters problem-solving skills, emphasizing how a thorough understanding of different functions can enhance analytical abilities. **Final Exam: Functions and Applications** The final assessment acts as a cumulative review of the course, allowing students to gauge their understanding and identify areas for further improvement. This exam encourages reflective learning, urging students to analyze their mistakes and grasp the conceptual nuances behind them. ### Course Strengths 1. **Comprehensive Coverage**: The course does an excellent job of covering a wide range of functions, ensuring that learners are well-versed in both common and uncommon types. 2. **Real-World Applications**: By emphasizing how functions are used in various disciplines, the course connects theoretical concepts to practical scenarios, enhancing engagement and relevance. 3. **Reflective Learning**: The final exam is designed to support self-assessment, allowing students to not just ascertain their knowledge but also to understand where they may require additional focus. ### Recommendations I highly recommend "Algebra: Elementary to Advanced - Functions & Applications" for anyone looking to strengthen their foundation in algebra, whether you're a high school student preparing for advanced mathematics, a college student needing to fill gaps in your knowledge, or a professional looking to brush up on your analytical skills. The course’s structured approach to functions, coupled with its support for reflective learning, will undoubtedly equip you with essential skills for both academic and real-world applications. ### Conclusion In summary, this Coursera course excellently encapsulates the essential principles of algebraic functions and their applications. With its thorough syllabus and practical focus, it stands as a commendable choice for learners at various levels. So, if you are interested in mastering algebraic concepts and enhancing your problem-solving skills, enroll today and take the first step towards algebraic proficiency!

Syllabus

Module 1: Introduction to Functions

A linear relationship between two variables occurs when there is a constant increase or constant decrease in one variable with respect to the other. Linear functions have the property that any chance in the independent variable results in a proportional change in the dependent variable. Many physical situations can be modeled using a linear relationship. Adding an extra term of the form ax^2 to a linear function creates a quadratic function, and its graph is the parabola. We will see examples of linear and quadratic functions and their applications in the sections that follow.

In the last module we introduced the important concept of a function and considered the linear and quadratic functions. In this module, we discuss methods for building new functions from those that are already familiar to use. One method will use the graph shifting techniques already introduced. These methods are developed further and applied to new functions. Constructing a graph is often an important first step in solving a problem. The more functions you can picture, the better problem solver you will be.

Congratulations on reaching the final exam! This final assessment will be cumulative in nature, covering all aspects of the course. Use this final as a teaching tool: justify what you know and identify areas for improvement. Use scrap paper as you take this final. Try to use any formula sheets or outside resources as a tool and not a crutch. Check your answers before you submit. After the test, review any incorrect answers to find your mistakes. Try to separate "silly" mistakes from the more substantial mistakes in understanding. Good luck!