Precalculus: Relations and Functions

Precalculus: Relations and Functions

This course is part of Precalculus through Data and Modelling Specialization

Instructor: Joseph W. Cutrone, PhD

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What you'll learn

Model data with both single and multivariable functions
Visualize and analyze data using different technologies.
Understand properties of different types of functions to apply them accordingly to model different situations.
Perform vector operations, such as addition, scalar multiplication, dot product, and cross product, to analyze geometry in space.

Skills you'll gain

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Assessments

9 assignments

Taught in English

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This course is part of the Precalculus through Data and Modelling Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 4 modules in this course

This course helps to build the foundational material to use mathematics as a tool to model, understand, and interpret the world around us. This is done through studying functions, their properties, and applications to data analysis. Concepts of precalculus provide the set of tools for the beginning student to begin their scientific career, preparing them for future science and calculus courses. This course is designed for all students, not just those interested in further mathematics courses. Students interested in the natural sciences, computer sciences, psychology, sociology, or similar will genuinely benefit from this introductory course, applying the skills learned to their discipline to analyze and interpret their subject material. Students will be presented with not only new ideas, but also new applications of an old subject. Real-life data, exercise sets, and regular assessments help to motivate and reinforce the content in this course, leading to learning and mastery.

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.

What's included

3 videos3 readings2 assignments

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.

What's included

5 videos2 readings3 assignments

5 videosTotal 82 minutes

Equations of Lines26 minutesPreview module
Quadratic Functions29 minutes
Function Composition12 minutes
Inverse Functions9 minutes
Graphs of Inverse Functions4 minutes

2 readingsTotal 60 minutes

Sample Problems: Equations of Lines and Quadratics30 minutes
Sample Problems: More Functions30 minutes

3 assignmentsTotal 90 minutes

Linear and Quadratic Equations30 minutes
Function Composition and Inverses30 minutes
Modules 1 and 2 Test - Functions30 minutes

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.

What's included

3 videos2 readings2 assignments

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.