Precalculus: Relations and Functions

Go to Course: https://www.coursera.org/learn/precalculus-relations-functions

Introduction

# Course Review: Precalculus: Relations and Functions on Coursera In the realm of mathematics, precalculus serves as a crucial stepping stone for students venturing into more complex fields like calculus, statistics, and various branches of science. The course "Precalculus: Relations and Functions" offered on Coursera is designed to provide students with a solid foundation in mathematical concepts that are pivotal for interpreting and modeling the world around us. Here's a detailed overview of the course, along with a review and recommendation for prospective learners. ## Course Overview The **"Precalculus: Relations and Functions"** course is structured to cater to a wide audience, emphasizing that its importance extends beyond those solely interested in pursuing further mathematics. The curriculum is divided into four comprehensive modules, each designed to unravel the complexities of functions and their applications. ### Syllabus Breakdown 1. **Module 1: Basics and Common Functions** - This introductory module lays the groundwork for understanding functions as essential tools in mathematics. Key concepts such as domain, range, and end behavior of graphs are explored. This module is vital as it prepares learners for more advanced topics and enhances their analytical skills in mathematical modeling. 2. **Module 2: Equations of Lines, Quadratics, and More Functions** - Building on the first module, this section delves into linear and quadratic functions, which are fundamental to real-world applications like revenue and cost analysis. Students will engage with graph identification and learn critical concepts such as function composition and finding inverses. 3. **Module 3: Exponential and Logarithmic Functions** - Here, students will expand their understanding by exploring exponential and logarithmic functions, essential in modeling phenomena in natural sciences and finance. The focus on inverse functions provides a deeper comprehension of functional relationships and their implications. 4. **Module 4: Properties of Logarithms** - This module completes the course with a thorough examination of logarithmic functions and their properties. Applying logarithms to real-world scenarios underscores their relevance and importance in various fields, particularly when dealing with growth and decay processes. ## Review of the Course The "Precalculus: Relations and Functions" course excels in its clarity and structure. Each module is thoughtfully designed, gradually building on the knowledge acquired in previous lessons. The interactive nature of the course encourages active participation, which significantly enhances retention and understanding of the material. ### Strengths: - **Accessibility:** The course is made for students of all backgrounds, making it inclusive for those who may not have a strong foundation in mathematics. - **Practical Applications:** Emphasis on real-world applications of mathematical concepts makes learning engaging and relevant. - **Quality of Instruction:** The course is delivered by experienced instructors who present the material in an easily digestible manner, using practical examples and visual aids. ### Areas for Improvement: - While the course is comprehensive, those with a stronger mathematical background might find certain sections a bit elementary. However, this is a minor critique given the course’s goal of providing foundational knowledge. ## Recommendation I highly recommend the "Precalculus: Relations and Functions" course for anyone looking to strengthen their mathematical skills, whether you are preparing for further study in science or simply wanting to enhance your analytical abilities for everyday problem-solving. The course’s practical approach ensures learners can apply mathematical concepts to real-world scenarios, a critical skill in today’s data-driven world. By completing this course, you will not only gain a robust understanding of precalculus concepts but also develop the confidence to tackle more advanced mathematics and scientific coursework in the future. Enroll now and take the first step towards unlocking the power of mathematics in interpreting the world around you!

Syllabus

Module 1: Basics and Common Functions

Functions help to study the relationship between two or more variables. They are the basic quantitative tool used to visualize, analyze, and interpret these relationships. Studying functions is the first step in developing analytics skills for mathematical modeling. In this module, we develop the concept of a function and review important algebraic operations on functions used later in this course. We will also study the important features, like domain, range, and end behavior of graphs.

In this module, we will study two common types of functions: linear and quadratic. We will learn how to identify common features of their graphs, and see how they can be used to model real world situations, particularly those involving revenue and cost. We will also further explore function compositions, and learn how to find the inverse of a function.

In this module, we expand our catalog of functions to study two new functions that arise when modelling natural phenomena: the exponential and logarithmic functions. In the last module, we saw that one-to-one functions have inverses, which reverse the function process. For example, the function f(x) = x^3 has as its inverse the function g(x) = x^(1/3). We now want to expand this process to find inverses for exponential functions - those of the form f(x) = a^x, where a is a positive number not equal to one.

Understanding the logarithm as an exponent allows for important algebraic properties of the logarithm. In this module, we will explore these properties and their uses as we apply logarithms to real world examples.