---
tags: mth225, dailyprep
---

# Daily Prep 3.3 -- MTH 225

## Overview

This lesson shifts the focus of Module 3 from sets to **functions**. If a set is the prototype for data structures, then a function is the prototype for programs. We'll be learning about what a function is (and what it is not), and the concepts of the **domain**, **codomain** and **range** of a function.

## Learning objectives

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught.

* State the definition of a function between two sets.
* Given a mapping between two sets, determine whether or not it is a function.
* Use function notation correctly.
* Represent a function as an arrow diagram, closed formula, or matrix.
* Given a function, state the domain, range, and codomain.

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class.

* Find values of a function defined recursively.
* Determine if the range of a function is equal to its codomain.
* Implement a simple mathematical process as a Python function and then deterine the domain, codomain, and range of the function.

## Resources for learning

**Video:** Watch this from [the MTH 225 playlist](https://vimeo.com/showcase/8667148):

<iframe title="vimeo-player" src="https://player.vimeo.com/video/614432178?h=4c99fd279a" width="640" height="360" frameborder="0" allowfullscreen></iframe>

**Text:** Read in the textbook, [Section 0.4](http://discrete.openmathbooks.org/dmoi3/sec_intro-functions.html) up to, but not including Example 0.4.5.

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

## Exercises

Once you have watched the videos above, go to this form and complete all the non-optional items on it:

https://docs.google.com/forms/d/e/1FAIpQLSeqzM88tpL-z1XZ_1-5Ae6RnQ_51mQlrHnWCOOUBVu3CtBr7g/viewform

## Submission and grading

**Submitting your work:** Your work is submitted when you submit the Google Form. You should receive an email receipt indicating that the work was submitted successfully.

**How this is graded:** The pre-class portion of the Daily Prep is graded either 0 points or 1 point, on the basis of completeness and effort. Wrong answers are not penalized. Earning a "1" requires that you:

- Turn the work in before its deadline;
- Leave no item blank or skipped, even accidentally; and
- Give a good-faith effort at a correct answer on every non-optional item.

More information can be found in the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document.

When you arrive for the class meeting, you'll be put into a group of 2-3 to complete a quiz over this material, which will be graded on a 0/1 scale on the basis of correctness.