Functions in Python can have optional parameters. Functions with optional parameters can be called with or without passing an argument through the optional parameters. If no argument is provided, the default value will be passed through the parameter. The default value must be defined with an = sign in the function header. For example, in the function rotate(x, y = 3), y is an optional parameter with a default value of 3.

Optional Parameters

Python's `typing` module defines standard notation for function and variable type annotations. These annotations make intended types explicit, improving code readability and providing a consistent way to document code.

Python `typing` Module for Type Annotations

In Python, function parameters refer to the variables that are listed within a function definition. For example, in the function rotate(x, y), the parameters are x and y.

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Function can be thought of as devices that take in material, perform a specified operation on the taken-in material, then output a resulting object. 

Inputs are referred to as arguments 
End result is referred to as output or return value. 

Functions in Python

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Runestone: Foundations of Python Programming

New functions can be created with the keyword def, as such:

```python
def sub(x, y):
   return x - y

def add(x, y):
   return x + y

def square(x):
    return x ** 2
```
 


Defining Functions in Python 

Functions are displayed and written in the following format:

- For one argument: functionname(argument)
- For two arguments: functionname(argument1, argument2)
- For three arguments: functionname(argument1, argument2, argument3)
- *And so forth 

Format of Functions in Python

The terms input and argument are often used interchangeably to refer to function arguments. However, the term "input" can also refer to the input() function. 

"Argument" will universally refer to information that is passed into a function as such: function(argument) 

Inputs vs Arguments in Python

Python comes with a host of built-in functions. Here are some examples:
- print()
- input()
- id()
- range()
- abs()
- bin()
- bool()
- len()
- round()
- pow(x,y,z)
- chr(i)
- slice()
- ord()
- hex()
- oct()
- int()
- float()
- str()
- open()



Built-In Functions in Python

Which of the following are true about functions in Python? (choose all that apply)

Lambdas are shorthand function definitions. A lambda function is a small anonymous function. A lambda function can take any number of arguments, but can only have one expression. The syntax is, lambda arguments : expression. For instance,

```python
func = lambda x, y : x + y
```

defines a Python function that takes two arguments (which must support the + operator) and returns their sum/concatenation.

Lambdas in Python

Example of the square function:
- ```square(4)``` --> 16

Example of the subtraction function:
- ```sub(6, 4)``` --> 2

Example of the square function in a multidimensional problem:
- ```sub(square(3), square(4))``` --> -7 

Example of the print function:
- ```print(3)``` --> *Integer 3 will actually display on output screen. 

Examples of Python Arithmetic Functions 

A Python generator is a special type of function that returns a lazy iterator. Instead of computing and storing all values in memory at once, a generator produces one value at a time using the `yield` keyword, pausing its execution state between calls. This memory-efficient approach makes generators highly effective for processing large datasets, such as in deep learning data loaders where they iteratively yield a single data batch without loading the entire dataset into memory.

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