Functions
Functions
Simple descriptions of what a function is, what to think of as a function, how we write functions, what they are used for, and wherever we may encounter the term function. Classical mathematical functions with special notation are also shown in the article.
Properties of a function
Basic knowledge of functions, definitions and an overview of the properties of functions including examples and graphs. You will learn what the defining domain of a function is and the domain of values, when a function is increasing and decreasing, whether it is even or odd, or whether it is prime or has a minimum and maximum. The definition of a bounded and inverse function has not been forgotten.
Definitional scope
What is a defining domain, what is it used for and how is it calculated. Decomposing functions into outer and inner functions and not missing the calculation of definitional domains for composite functions.
Inverse functions
The definition of an inverse function and a detailed explanation of what an inverse function is and how to calculate it.
Even and odd functions
Description and definitions of even and odd functions. Basic properties, graphs of even and odd functions, and verification methods.
Linear functions
A short chapter on a simple linear function. Types of linear functions and their properties are described. There are also sample graphs of each function.
Powers
Basic concepts about powers, followed by an explanation of what to do when we encounter a negative exponent or exponent in a fraction. Part of the chapter is devoted to square roots, although square roots are again just ordinary powers. There are also special cases you may encounter when counting with fractions and patterns.
Roots
What is a square root, how to solve examples with square roots, description and definitions.
Logarithms
A description of the exponential function that is necessary to understand the logarithmic function. There are graphs of logarithmic and exponential functions, as well as basic and most used theorems about logarithms.
Quadratic functions
Properties and typical features of quadratic functions, demonstration of calculating vertex coordinates using the method of completing on squares. Examples of different types of graphs of quadratic functions are also included.
Exponential functions
What is an exponential function, what are its properties
Goniometric functions
Basic concepts about triangles, relationships between angles, describing goniomtric functions in the special case of right triangles. The inverse of the arcus function is also mentioned and the unit circle is introduced and the arc measure of an angle - the radian - is explained. The sine and cosine theorem.