Linear Equations: Relations and Functions Part 1

Linear Equations: Relations and Functions

​Lesson Target

Students will be able to ​Recognize a relation as a set of ordered pairs that relates an input to an output, and a function as relation for which there is exactly one output for each input, using tables by completing a quizizz lecture activity.

Fill in the Blanks

The seventh grade class is planning a field trip. There are two proposals, one to a bowling alley and one to the Omni Theater. To make the best choice, the students have to do some research.

Casey and his friend Max are in charge of researching different bowling alleys to find the best price. They find out that the local bowling alley that is closest to school has a very good offer. This bowling alley charges a flat fee for shoes and then a fee per game.

“I wonder how many games we will have time for,” Casey said to Max.

“I don’t know, but that will impact the cost,” Max responded.

“Let’s figure it out. What is the flat fee for shoes?” Casey asked.

“It is $2.00 and it is $3.00 per game,” Max said.

The two boys took out a piece of paper and began to figure out how much the total would be based on games.

Try and create an equation that would solve for the following problem?

​What is a function?

To solve the last problem, you will need to understand functions. A function is when one variable is impacted by another. In this case, there is a fee for shoes and a fee per game. The total cost per student will depend on the number of games. The cost is a function of the games. Learn all that you can and you will be able to figure out the fees at the end of the lesson.

​How did we get this crazy mess?

​Relations and Functions: Recognizing Relations and Functions​

​In this lesson, we will learn to recognize a relation as a set of ordered pairs that relates an input to an output, and a function as relation for which there is exactly one output for each input, using tables.

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When we work with relations and functions, we work with the world of relationships. We look at how one factor impacts or effects another factor.

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What is a relation?

A relation is written as a set of ordered pairs where one value is equal to x and one value is equal to y. What we are really looking at with a relation is the relationship between one factor and another. Let’s think about an example.

​Relations and Functions: Recognizing Relations and Functions​

Draw

Draw out a relation for motorcycles to motorcycle tires on a 2 cycled motorcycle using your own chart?

​Relations and Functions: Recognizing Relations and Functions​

​A motorcycle has an ordered pair of bikes to tires as (1, 2).

This means that for every one motorcycle there are two tires. This is a relation.

Draw

Create a relation between the number of cars a company can sell compared to the number of tires each car has...

​Relations and Functions: Recognizing Relations and Functions​

​A car has an ordered pair of cars to tires as (1,4).

This means that for every one car that is built, there are four tires. This is a relation.