## Functions versus Relations (Solutions Included)

#### Aligned To Common Core Standard:

**High School Interpreting Functions** - HSF-IF.B.5

How to Determine If a Relation is a Function - Functions, relations, expressions, sequences, everything seems like a ball of confusion. But don't worry! Here, we will take a look at what relations are, what is a domain, a range, and how to determine if a relation is a function. In mathematics, the relationship between a set of values, or a set of ordered pairs is known as a relation. In the ordered pairs, the set which has the first member of every ordered pair is known as the domain. The set that contains pairs of second members in the given sets is known as the range. To determine if a relation is a function, the easiest way is to create a table of the ordered pairs. Once you make pairs, the next step should be where you conduct a test to understand whether every element in the domain matches with exactly one element in the range. If the results match, then your relation is a function! These excellent worksheets and lessons help students quickly learn the differences and uses of both functions and relations.

### Printable Worksheets And Lessons

- Is the Relation a Function
Step-by-step Lesson- We learn the correlation between relations
and functions.

- Guided Lesson -
You will start to work with graphs instead of tables here.

- Guided Lesson Explanation
- In most cases, it is best to work with the ordered pairs first.

- Practice Worksheet
- You need to identify the domain, range, and if the ordered pairs
equate to a relation that is a function.

- Matching Worksheet - There is a a nice aspect to these problems that require you to critical think more than straight problems.

#### Homework Sheets

These require that in addition to determining is a relation is a function that you find the range and domain as well.

- Homework 1 - Determine if the relation is a function. Make sure to identify the domain and range.
- Homework 2 - If we check the ordered pairs we can determine if every x value maps to just one y value.
- Homework 3 - The domain tracks to the x value.

#### Practice Worksheets

They look like different version of the same material, but each is progressively more difficult.

- Practice 1 - Determine if the relation is a function. Make sure to identify the domain and range.
- Practice 2 - What is the range here?
- Practice 3 - X-value maps to exactly one y-value except.

#### Math Skill Quizzes

We add a few five pointers in these to see if students get swayed.