Function

“

Norfolk Southern, what's your function?

”

A function is basically some thing in which one $y$ value is assigned to one $x$ value. Everything has a function, from hearts beating to engines vrooming.

Types

Constant

$f (x) = y$

$y$ remains constant.

Identity function

$f (x) = x$

Here is where the function identifies itself.

Absolute value function

$f (x) = | x |$

This function forms an endless V. V for Vendetta, perhaps?

Quadratic function

$f (x) = x^{2}$

In this example, the function is smiling. How joyous!

Cubic function

$f (x) = x^{3}$

This time, the function is feeling all emotions at once. Maybe it's solving a Rubik's cube.

Square root function

$f (x) = \sqrt{x}$

I think this function is getting slightly more complex.

Square root function

$f (x) = \sqrt[3]{x}$

This is like the square root function, albeit mirrored in all axes.

Reciprocal function

$f (x) = 1 / x$

The interesting part of a function is that in some particular value, $f (x)$ = undefined, resulting in incredibly steep slopes or something. This is called an asymptote.

Reciprocal squared function

$f (x) = 1 / x^{2}$

This one is like a reciprocal function, albeit squared.

Step function

heck i can't get the secret formula

This one is like a staircase because it only focuses on real numbers.

Inverse functions

For every^[wrong] function, there is an inverse function. Just swap $x$ with $y$ , solve for $y$ , and boom.