# 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 $$(0, \infty)$$.