This comprehensive precalculus course, "Precalculus: Relations and Functions," provides the foundational knowledge necessary to utilize mathematics in modeling, understanding, and interpreting the world. It equips students with the essential tools required to embark on scientific careers and prepares them for future science and calculus courses.
Through an in-depth study of functions, their properties, and applications to data analysis, this course enables students to model data using single and multivariable functions. Additionally, it delves into the visualization and analysis of data using various technologies while exploring the properties of different types of functions to apply them in modeling diverse situations.
Furthermore, the course introduces students to vector operations, including addition, scalar multiplication, dot product, and cross product, to analyze geometry in space. Real-life data, exercise sets, and regular assessments are incorporated to motivate and reinforce learning, facilitating mastery of the course content.
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This course is divided into four modules. The modules cover the basics and common functions, equations of lines, quadratics, exponential and logarithmic functions, as well as properties of logarithms, preparing students for further mathematical and scientific studies.
The first module, "Basics and Common Functions," provides a fundamental understanding of function basics, graphing websites, and common functions. It offers multiple opportunities to practice sample problems, reinforcing the learned concepts.
The second module, "Equations of Lines, Quadratics, and More Functions," delves into equations of lines, quadratic functions, function composition, and inverse functions. It also includes a test to assess the understanding of the concepts covered in the first two modules.
Module three, "Exponential and Logarithmic Functions," focuses on exponential functions, logarithmic functions, and the natural logarithm. Students engage in sample problems and dedicated practice sessions to solidify their comprehension.
The final module, "Properties of Logarithms," explores the properties of logarithms and offers practice problems to reinforce learning. It also includes a test to evaluate the understanding of exponential and logarithmic functions covered in the third and fourth modules.
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