# Relations and Functions Worksheets

Mathematics is all about functions, operations, and relations between variables. They are a huge part of mathematics; in fact, there wouldnâ€™t be the concept of mathematics if there were no functions or relations in mathematics. Having said that, many students are not aware of these concepts, which can be applied to many different forms of math. A relation consists of a set of inputs and outputs. The relation shows that the input is somehow related to the output. An ordered pair is a set of inputs and outputs and represents a relationship between the two values. We can represent a relation in mathematics by using ordered pairs. This concept explains that two quantities have an impact on each other. Coming to functions, a function is a relation in which no input relates to more than one output. It means that a function is a relation with one output for each input. However, what distinguishes a function from a relation is that each x value in a function has ONE y-value. So, if a relation has ONLY ONE y value for each x value, this relation is a function. On the other hand, if a relation has TWO distinct y values 'a' and 'c' for the same x value of '5', it is a function.

### Aligned Standard: HSF-IF.A.1

- Range of Relations Step-by-step Lesson- You are given a relation that is graphed for you and are asked to find the range.
- Guided Lesson - It is all about determining if a relation is a function or vice versa.
- Guided Lesson Explanation - There are simple guiding principles that you can use here to determine if it is a go.
- Practice Worksheet - I give you a whole bunch of domains and ranges. You are then asked to identify the functions that are described.
- Matching Worksheet - You we review the three key skills for this section.

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

### Homework Sheets

Find the range of relations, if it is a function, and using the vertical line test.

- Homework 1 - The range of them consists of a set of y-coordinates. To find the range, find the y-coordinates.
- Homework 2 - A relation is a function if each number in the domain is paired with exactly one number in the range.
- Homework 3 - You can use the vertical line test on a graph to determine whether a this holds true.

### Practice Worksheets

Work on all three key skills for this topic.

- Practice 1 - This worksheet is really cool it covers things with integers and with the help of graphs.
- Practice 2 - Use the domain values in the table to determine the nature of this range.
- Practice 3 - If the domain value is paired with multiple range values, the relation is not a function.

### Math Skill Quizzes

The quizzes only have four questions due to the amount of space that the graphs take up.

- Quiz 1 - What is the range of this relation? You will then analyze a graph. Step by step explanations are given.
- Quiz 2 - The vertical red line intersects the graph in two places, so the relation is not a function.
- Quiz 3 - What's up with that relation. Express it as an understandable range.

### How Do These Classifications of Data Appear in the Real World?

Functions are more like automatic processes where you put in an input value and then a calculation based on the function produces an output. A series of ordered pairs is a relation. They can be functions if they have only one input and one output. If that holds true, the x coordinate is called the domain. It serves as the input and the y coordinate serves as the output. There are many different applications of these in the real world. Just about any type of measurement conversion is based on a similar principal. In North America we commonly measure temperature in units of centigrade or Fahrenheit. When we need to convert from Celsius to Fahrenheit, we can use the equations ((Degrees Celsius) x (9/5)) + 32 = Degrees Fahrenheit. This is simple of example of a function that we use every day. Basically, any fixed equation that we use will satisfy this. That would include most forms of economic principles such as calculating how much you earn year week based on a salary or hourly rate. Equations that calculate the patterns also would follow this series. If you have some form of mathematical operation that has one input and a matching output, guess what you are working with?

### When Relations Are Not Functions

If we remember back, this relationship only exists a single input results in a single output. If an input can lead to multiple outputs, than a function is not present. There are many things that we think exhibit this behavior in the real world, but simply do not. Actually, while doing research for this piece, I found several textbooks cite the amount of time spent studying as a function of the result on an examination or test. This could not be further from the truth. I studied like crazy for my Calculus and Differential Equations classes. Almost twice as much as my roommate, but she always out performed me on the exams.