Let's start by discussing how it's done.

### Syntax

### Basic Syntax

Here's a very simple Python function, that implements the mathematical function

$f(x) = 2 x + 1$

print(new_abs_function(-3))

```

Note that a function can have arbitrarily many `return` statements (including zero).

Execution of the function terminates when the first return is hit, allowing

code like the following example

```{code-cell} python3

def f(x):

if x < 0:

return 'negative'

return 'nonnegative'

```

Functions without a return statement automatically return the special Python object `None`.

### Keyword Arguments

```{index} single: Python; keyword arguments

* Any object can be passed to a function as an argument, including other functions.

* A function can return any kind of object, including functions.

We already {ref}`gave an example <test_program_6>` of how straightforward it is to pass a function to

a function.

Note that a function can have arbitrarily many `return` statements (including zero).

Execution of the function terminates when the first return is hit, allowing

code like the following example

```{code-cell} python3

def f(x):

if x < 0:

return 'negative'

return 'nonnegative'

```

Functions without a return statement automatically return the special Python object `None`.

### Docstrings

```{index} single: Python; Docstrings

```

Python has a system for adding comments to functions, modules, etc. called *docstrings*.

The nice thing about docstrings is that they are available at run-time.

Try running this

```{code-cell} python3

def f(x):

"""

This function squares its argument

"""

return x**2

```

After running this code, the docstring is available

```{code-cell} ipython

f?

```

```{code-block} ipython

:class: no-execute

Type: function

String Form:<function f at 0x2223320>

File: /home/john/temp/temp.py

Definition: f(x)

Docstring: This function squares its argument

```

```{code-cell} ipython

f??

```

```{code-block} ipython

:class: no-execute

Type: function

String Form:<function f at 0x2223320>

File: /home/john/temp/temp.py

Definition: f(x)

Source:

def f(x):

"""

This function squares its argument

"""

return x**2

```

With one question mark we bring up the docstring, and with two we get the source code as well.

We will give examples of how straightforward it is to pass a function to

a function in the following sections.

### One-Line Functions: `lambda`