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#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# Function Transformations

Transformation is one of the most important concepts for mathematical functions. As suggested by the name of the term, a transformation of a function is the output we obtain after putting the returned value of a function through a specific transformation technique such as a shift or a scaling. In the most general sense, we can think of this process as a composite function: putting the output of one function through another function. However, there are specific types of functions that are commonly used as transformations due to their particular characteristics and usefulness, and we will go through them in the following subsections, starting with shifting.

Since a transformation is most easily understood in the context of the changes that it applies to the plot of a function, we will also frame our following discussions accordingly.

## Shifts

A shift of a function happens when the plot of a function is shifted by a specific amount along the x axis and...