Question

1. identify two differences between using a python built-in function (e.g. abs) and a function from the math module.

Explanation:

1. Import Requirement: Python built - in functions like abs can be used directly without any import statement. For example, we can write print(abs(-5)) right away. However, functions from the math module, such as math.sqrt, require us to first import the math module (e.g., import math or from math import sqrt) before we can use them.
2. Input Type Handling: Built - in functions often have more flexible input type handling. The abs function can take an integer (e.g., abs(-3)), a float (e.g., abs(-3.14)), or even a complex number (in Python, the abs of a complex number a + bj is calculated as $\sqrt{a^{2}+b^{2}}$, like abs(3 + 4j) will return 5). On the other hand, most functions in the math module are designed to work mainly with floating - point numbers. For instance, if we try to use math.sqrt with an integer that is a perfect square, it will return a float (e.g., math.sqrt(4) returns 2.0), and if we try to use it with a negative integer, it will raise a ValueError (since the square root of a negative number is not a real number, and the math module deals with real - valued mathematics in general).

Answer:

1. Built - in functions (e.g., abs) can be used directly without importing, while math module functions (e.g., math.sqrt) need the math module to be imported first.
2. Built - in functions like abs can handle multiple numeric types (int, float, complex), while most math module functions are mainly for floating - point numbers and may raise errors with inappropriate input types.