# Solving Function Tables Worksheets

A function is a rule that designates a fixed input to a fixed output. For every different input there is there is a unique corresponding output. We can represent the various inputs and outputs of functions in the form of a function table. This is just one of several different methods that we can use to describe a function, but it is highly effective for communicating them to other people. These worksheets and lessons show students their way around function tables and their uses. The have a great number of applications that can help you describe processes quicker and easier.

### Aligned Standard: 8.F.A.1

- Tables Step-by-Step Lesson- We give you a rule set and an x,y table. Go crazy!
- Guided Lesson - More rules and more tables. This thing just got out of control!
- Guided Lesson Explanation - This is a plug and chug activity as they called it in my linear algebra class.
- Independent Practice - This sheet will help you perfect the skill to a "T", or is it tee?
- Matching Worksheet - Match the rule sets and tables to their completed versions.

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

### Homework Sheets

Some tables are completely empty on the y-value, some have a few entries.

- Homework 1 - We have to complete the table to show how to fill the y block. We will use the equation y = 4x to complete the table.
- Homework 2 - Make sure to get rid of all operations first and then proceed.
- Homework 3 - Just a few missing values are in this function table.

### Practice Worksheets

I always like to try to give students one complete problem. It helps those that struggle to grow.

- Practice 1 - Complete the function table for each equation. Input the x value into each equation to determine the end y value.
- Practice 2 - In each case, you will need to solve for y, but it is just a plug and chug equation.
- Practice 3 - Reverse engineer the given value to make sure the function is properly functioning.

### Math Skill Quizzes

The quizzes follow the same scheme that can be seen with the homework and practice sheets.

- Quiz 1 - Some are missing three values and other are missing four. If you forgot how these work, you can use the completed problems to help you better understand it.
- Quiz 2 - Completely blank y values. There is no help given with this quiz.
- Quiz 3 - As normal, we save quiz 3 for the negative values. There is one sample value worked out for you.

### How to Solve Function Tables

A function table represents the inputs and their respective outputs based on a given function that the input passes through. Function tables can be represented in both vertical and horizontal orientations in depends on which best suits your situation. In this lesson, we will take a horizontal approach. So, in the examples that we have, the functions will be displayed in two rows. One row will display the input and the other will be displaying the output functions.

Let's take example of selling or buying candy bars. We can represent that function in the form of a table. If candy bars cost $2. We can represent this in a simple equation like this: c = 2x. In this equation c would indicate the table cost and x would be the number of candy bars you could buy or sell. We can then present this in a function table to give us a series of prices that we can refer to when selling the candy.

This could be helpful for you to instantly know the price when a customer buys different numbers of candy bars. You would just take a quick glance at this table, and you would know how much to charge them. The c value indicates the number of dollars ($). We recognize that if we only have $4to spend, we can only buy 2 candy bars.

**Function Table Rules** - Each function is a rule, so every single function table has a certain rule that defines the relationship that exists between the output and the input. Sometimes a rule is best described in terms of the words and in some cases the best way to define it is by using an equation.

### How Does This Skill Apply to Everyday Life?

Over the course of the average day you come in contact with machines that are constantly processing values through a function table and you probably do not even realize it. If you have used a vending machines to buy a bag of chips, a bottle of water, or to make your favorite coffee this type of math was involved for the machine to understand that you input enough money to make a valid transaction. You will continue to put coins or bills into the vending machine until you satisfy the rule to make the purchase. If you have ever calculated your weekly salary for a job, you have used this form of math. It is a direct function between your hourly pay rate and the number of hours that you performed the job. If you own a mobile phone that does not have an unlimited plan, the pricing is based on this form of math as well. This a more complex rule because there is a flat monthly charge and then a charge associated with number of calls or text messages that you make over the course of a month. If you think about it the number of different situations that this can be directly related to is boundless.