# Input and Output Worksheets

In math there are mathematical relationships called functions that create outputs when given a set of inputs. If you think of functions as machines, you can quickly get the picture of what they do. Just like the bread machine on your kitchen counter, if you give it all the needed ingredients (input), the machine (function) will produce or create delicious bread (output). Functions often take on the form of f(x). In this section you will work with a series of function tables that consist of inputs, outputs, and the governing rule. You can use two of these values to manipulate the tables to determine the variable of interest. Also note that if you know a series of inputs and outputs, given enough data, you can determine the rule that governs that system. These worksheets and lessons will help you feel more confident with working with inputs and outputs. You will also learn how to determine the governing rule of a system based on them.

### Aligned Standard: Grade 8 Functions - 8.F.A.1

- Function Tables Step-by-Step Lesson- Drop in the x value and what comes out for f (x).
- Guided Lesson - Interpret rates of graphs, graph functions, complete f(x) tables.
- Guided Lesson Explanation - Each problem pretty much required its own page.
- Independent Practice - I feel that I really covered this standard and skill very thoroughly. Let me know if there is anything I can add.
- Matching Worksheet - The problems in this sheet are very diverse allowing for a little bit of ease when choosing matching problems.

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

### Homework Sheets

This is a core skill that students need to master quickly for future material.

- Homework 1 - Complete the table. f(x) = 3x
- Homework 2 - The graph of the function is the straight line connecting the pairs.
- Homework 3 - Choose points to complete the data table.

### Practice Worksheets

If students had trouble understanding how to interpret graphs before, this will cure them.

- Practice 1 - This graph shows how the number of cookies box depends on the number of days that Kenny baked. If Kenny bakes cookies 3 day, how many cookie boxes will be ready?
- Practice 2 - This graph shows the charging level (%) of a battery decreasing over several hours. How much (%) battery life will remain after 12 hours?
- Practice 3 - This graph shows the fuel level (%) in a fuel tank over time. What percent (%) of the fuel will remain after 8 hours?

### Math Skill Quizzes

You will definitely need some graph paper for these.

- Quiz 1 - Graph this function.
- Quiz 2 - Interpret the graphs to answer the questions.
- Quiz 3 - This graph shows numbers of workers that worked over a 7 day period. How many workers were working on the 3rd day?

### What are Inputs and Outputs of Functions?

We all know that plants are the primary source of our oxygen. They take in carbon dioxide and give out oxygen. Just like that, in mathematics, the manufacturing of something from nothing can be something called a function. One thing goes in, and another one comes out. They are truly like little mathematical machines that rely on an input to get an output.

Functions exist everywhere and all around us. We eat food, and we get energy. We switch on the TV, and we can watch our favorite channel. We ask somebody a question, and we get an answer. We push a key on a keyboard or on our phone and something happens on a screen.

An expression that produces exactly one answer for any given number that we provide the expression with is called a function. There are two main components to a function.

**Input** - When we input a number in an expression, it is called an input. This is kind of like the ingredients needed for a recipe. When you have these ingredients present, you get the next part.

**Output** - The answer we get after the calculations are finished, is called output. The output is kind of like the results of creating a dish from a set of ingredients.