Functions

A function \(f\) from a set \(D\) to a set \(Y\) is a rule that assigns a unique value \(f(x)\) in \(Y\) to each \(x\) in \(D\).

The set \(D\) of all possible input values is called the domain of the function. The set of all output values of \(f(x)\) as \(x\) varies throughout \(D\) is called the range of the function. The range might not include every element in the set \(Y\).

Even and odd functions

A function \(y = f(x)\) is an
even function of \(x\)  if \(f(-x) = f(x)\)
odd function of \(x\)  if \(f(-x) = -f(x)\)
for every \(x\) in the function's domain.

The graph of an even function is symmetric about the y-axis.
The graph of an odd function is symmetric about the origin.

\(f(x) = 0\) is even and odd function

Linear functions

A function of the form \(f(x) = mx + b\), where \(m\) and \(b\) are fixed constants, is called a linear function.

Power functions

A function of the form \(f(x) = x^a\), where \(a\) is a constant is called a power function.

Exponential functions

A function of the form \(f(x) = a^x\), where \(a > 0\) and \(a \ne 1\), is called an exponential function (with base a). All exponential functions have domain \((-\infty, \infty)\) and range \((0, \infty)\).