Functions

You can think of absolute value as a way to always make a number positive, no matter if it is positive or negative. The absolute value of a number is the distance from that number to zero, no matter which direction you are from zero.

To classify functions, we look at how the output changes based on the input. Different ways to classify functions are: linear functions, quadratic functions, exponential functions and logarithmic functions.

A function is like a machine that takes in a number (or an "input"), does something to it, and gives you another number (or an "output"). A function is a mathematical concept that maps a set of inputs, called the domain, to a set of outputs, called the range. It defines a unique output for each input in the domain. The relationship between the inputs and outputs is often described using an equation or a set of rules. In mathematical notation, a function is typically denoted by f(x), where x is an input and f(x) is the corresponding output. Functions can be used to model real-world situations and can help to simplify complex problems.

A transformation in mathematics refers to a process or rule that takes an input and maps it to an output, changing its position, size, or shape. Transformations can be thought of as operations performed on geometric objects such as points, lines, and shapes, to produce a new image or figure.