# Functions versus Relations Worksheets

Understanding the differences between functions and relations is often very confusing for students. because there is a great deal of crossover between the two. A relation is a link between the elements of two sets. The elements in those sets can be values or expressions. Functions are a very specific relation where one element of one set is mapped to work directly with a specific element of another set. This is a static relationship where the two things between the sets are statically linked. Relations are based on the cartesian product of the sets. These excellent worksheets and lessons help students quickly learn the differences and uses of both functions and relations.

### Aligned Standard: HSF-IF.B.5

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

- Quiz 1 - You will need to prove it one way or another.
- Quiz 2 - See if this one works out for you.
- Quiz 3 - I can usually find some simple answers with this quiz.

### What are Relations?

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. Relations can come in many different forms such as equations, diagrams, or even lists of elements. Relations can exhibit both a static or dynamic output where what we input either does or does not always have the same result.

### What are Functions?

A function is a specific type of relation where every input corresponds to a fixed single output. This output and input value could be a number, or any type of element found within a set. The foundational concept to remember here is that functions are static relationships, what comes out does not change. We can also say that all functions are relations, but not all relations are functions.

### How to Determine If a Relation is a Function

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! Some dead give aways are when you see a linear equation that you know clearly designates a line that you could graph. Linear equations are functions because they offer fixed output.