Polynomial Functions

Polynomial functions follow the pattern $f(x) = a_nx^n + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + ... + a_2x^2 + a_1x + a_0$ where $a_n$ are real numbers, $n$ is a whole number and $a_n \neq 0$ Examples of polynomial functions include:
$f(x) = 7x^3 + 5x^2 + 10x + 2$
$g(x) = 9x^5 - 8x^2 + x - 15$

Function Definition

A function has one y-value for every x value.
The points {(3, 1), (2, 4), (-5, 0)} form a function with a domain of {x|-5, 2, 3} and a range of {y|0, 1, 4}. There exists one y value for each x value.
The points {(2, 5), (3, 7), (2, 2)} do not form a function since for the x value of 2, there are two y values. The domain and range can still be mapped as {x|2, 3} and {y|2, 5, 7} respectively. When a set of points is not a function, it can still be a relation (maps input values to output values, usually $x \to y$)

Vertical Line Test

Any relation that satisfies the vertical line test is called a function.

Power Functions

Power functions are a special case of polynomial functions containing only one term. They come in the format of $y = ax^n$ where $n$ is a whole number.

Even and Odd Functions

If the degree of a power function is even, then the function is even. If the degree of the power function is odd, then the function is odd.

$y=x^2$ is an example of an even function

$y=x^3$ is an example of an odd function