Question

Write the following functions and provide a program to test them. a. def smallest(x, \(\left.y_{,}, 2\right)\) (returning the smallest of the arguments) b. def average \((x, y, z)\) (returning the average of the arguments)

Short answer

Define 'smallest' with `min`, 'average' with sum/3, and test with example inputs.

Step-by-step solution

Define the 'smallest' function

Create a function named `smallest` that accepts two arguments, `x` and `y`. Use the `min` function to find and return the smaller of the two numbers.

Define the 'average' function

Create a function named `average` that accepts three arguments, `x`, `y`, and `z`. Calculate the sum of these arguments and divide by 3 to return their average.

Write a test program

Write a simple test program to verify the correctness of both functions. For `smallest`, test with numbers like 3 and 5. For `average`, test with numbers 4, 7, and 10. Print the results to check if the functions work as expected.

Implement 'smallest' in code

```python def smallest(x, y): return min(x, y) ```

Implement 'average' in code

```python def average(x, y, z): return (x + y + z) / 3 ```

Implement the test program

```python def test_functions(): # Test smallest function print(f"Smallest of 3 and 5: {smallest(3, 5)}") # Expected: 3 # Test average function print(f"Average of 4, 7, and 10: {average(4, 7, 10)}") # Expected: 7 test_functions() ```

Key concepts

Defining Functions

Defining functions in Python is both a powerful and essential skill. A function allows you to encapsulate a block of code, giving it a name and allowing it to be reused anywhere in your program.
This makes your code modular, tidy, and easier to manage.

To define a function, you use the `def` keyword, followed by the function name and parentheses `()` containing any parameters the function might take.

• Example: To define a function `smallest` that takes two parameters `x` and `y`, you would write:
  ```python def smallest(x, y): return min(x, y) ```

You may notice the colon `:` at the end of the function header, which signifies the start of an indented block of code that belongs to the function.
Within this block, you can define the logic of the function and use a `return` statement to send back a value to the caller of the function. Functions can take multiple parameters, such as the `average` function, which takes three parameters `x`, `y`, and `z` and calculates the average of these numbers.

Remember, the key advantage of functions is reusability. Once written, you can call a function any number of times with different arguments, which saves time and effort by avoiding redundancy.

Testing Functions

Testing functions is a crucial part of programming, ensuring your code works as intended. When you create a function, you should also create tests to verify that function's behavior.

One simple way to test functions in Python is by writing small test programs that call your functions with sample inputs, checking their outputs against expected results.

• Example: If you want to test the `smallest` function, you can call it with numbers like 3 and 5 and check if it returns 3:
  ```python print(f"Smallest of 3 and 5: {smallest(3, 5)}") # Expected: 3 ```
• Similarly, test the `average` function with numbers 4, 7, and 10 to see if it returns 7 as expected:
  ```python print(f"Average of 4, 7, and 10: {average(4, 7, 10)}") # Expected: 7 ```

Good tests are precise and cover different edge cases.
It's always a good practice to write tests before using the functions in larger programs, ensuring they handle expected and unexpected inputs gracefully.

Python also offers testing frameworks, like `unittest` or `pytest`, which provide more robust and automated ways to test your code, especially useful for larger projects.

Arithmetic Operations

Arithmetic operations form the backbone of many computational tasks, and Python makes performing these operations straightforward.

There are basic arithmetic operators you'll frequently use: addition (+), subtraction (-), multiplication (*), and division (/).
These operators can be combined to perform more complex mathematical computations.

In the `average` function, we perform arithmetic operations by first adding the three input arguments using the `+` operator, and then dividing the sum by the number of inputs, which is 3:
```python (x + y + z) / 3 ```
This formula computes the average of three numbers.

• Important note: Division in Python will always return a float, even if you divide two integers.

Python follows operator precedence, meaning that certain operations are performed before others (for example, multiplication before addition).
You can control the order of operations using parentheses `()`, which ensures that the operations inside them are performed first.

Understanding and correctly applying arithmetic operations are foundational skills you'll apply repeatedly in any programming project.