This series of function table worksheets can be used to help you practice solving various algebraic expressions using known tables and a given rule. Each problem contains different values for the variables within the stated rule. You will learn how to determine the math rules that are demonstrated by the inputs and outputs of a function. We will also have you process inputs when given a function. You also be flipped upside down and be asked to predict inputs that are required to create the given outputs. On this page are lessons, worksheets, and quizzes demonstrating how to deal with function tables. Learn how to evaluate and complete the tables based on a given rule (equation).
Print Function Tables Worksheets
Click the buttons to print each worksheet and associated answer key.
Function Tables Lesson
This will walk students through solving a full on problem. They will be given a rule to put into place and they will determine outputs based on that rule.
Practice Worksheet
Calculate the required values and fill the output fields using the rule stated above the tables. You will be given an example and then asked to complete 2 practice problems.
Practice Worksheet 2
All of the rules that are applied within these problems are very basic. The goal of this worksheet is just to help get kids into a rhythm with this skill.
Variable Tables Worksheet 1
For each problem you will determine the rule followed by each function table. They can apply and follow any series of operations.
Worksheet 2
The rule consists of 2 variables using Addition, Division, Multiplication, and/or Subtraction.
Known Tables (2 variables-input only) Worksheet 1
You will just need to place the input in there and see what the output will be.
Output Tables Worksheet 1
You are given the output will these problems and you must determine what input created it. So we are working in reverse.
Reverse Tables Worksheet 2
You will work backwards again. You are given an output and you need to determine the input.
3 Variables Inputs Worksheet 1
The inputs will have 3 operations applied to them. See what you think.
Missing Elements Lesson
Learn how to complete tables when there are missing elements on either side of the inputs and outputs.
Missing Elements Practice
Calculate the required value and fill in the blanks of either A or B each time using the rule stated above the table. Rule: B = A x 4
Put It Together Worksheet
Using the rule and a reference input or output, determine what is missing to complete the ful function table.
Missing Parts Practice
This is where it starts to get a little easier to do after you have had a good amount of practice.
Empty Warm Up
Three problems for you to work on as a class. These are incomplete function tables that you must complete.
Tables with Missing Elements Lesson
This is very similar to the previous lesson, just a great deal more basic.
Basic Skill Worksheet 2
Complete each of the tables based on the rules are given. These are very simple problems.
Missing Elements Practice Worksheet
Practice handling function tables with missing elements by completing the problems below. Example: Find the least common multiple: Rule: a = b + 2
Skill Quiz
It is time to assess how well you are doing with this. This quiz will help you quickly determine that.
Missing Elements Review
This sheet makes for a nice class review sheet. Students will have the time to complete problems and a space is provided where they can write the completed problem.
Horizontal Function Tables Worksheet 1
We have you work on mixed variables to provide you with some clarity as to what is important in these problems.
Both Sides of the Equation
Practice this skill by completing the problems as quick as you can. There are 2 variables in each of the equations that are presented. You need to determine how to get the other half.
Plug In Quiz
For each table, fill in the blanks based on the rule given. Then check your answers and add up your total score. Example: Rule: a = b + 3
What Are Function Tables?
As a student, have you ever wondered what are function tables and why are they important? They are an essential tool in mathematics and mathematical modeling. They allow us to take a function and input a range of values, outputting the results in a tabular format.
This is extremely useful for visualizing how a function behaves over a specific range or doing quick calculations without first graphing the function.
A function table is a method of demonstrating the outcome of a function. It provides you a list of subsequent input values and the after it runs through the function the output as a result of the input value. The tables are more often displayed in a horizontal orientation (left to right) but can also be found in vertical (up and down) alignments as well. Functions are set math rules that follow a predictable relationship between the input and the output. Functions can be used to describe plenty of dependent and independent math relationships. If you examine the relation between the inputs and outputs, you can determine the rule that is set in place by the function. You can also use the data provided in the table to predict future outcomes in the table. This is mathematically how some phenomenon in nature are described and explored. They provide us with basically a key to how a system works. I find it to basically be cheating, because all you have to do is plug in the numbers found within the table and its all down hill from there.
How They Can be Used?
Function tables are a way of representing a function's output for a given range of input values. To create a function table, we list the input values in a column and the corresponding output values in the next column. For example, let's say we have a function f(x) = x<sup>2</sup>. We could create a function table for this function by inputting a range of values for x and then calculating f(x) for each value:
| Input (x) | Output (f(x)) |
| -2 | 4 |
| -1 | 1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
As you can see, they can be very straightforward. They allow us to quickly see how a function behaves over a given range of input values.
Function tables can be used for more than just visualizing a function's behavior. They can also be used for quick calculations. For instance, if we wanted to know f(2), we could look at the function table and see that the output is 4. We don't need to graph the function or do any complicated calculations; we can just read off the answer from the table.
Examples of Using Functional Tables
Now that we know what they are and how to use them, let's look at some examples.
Example 1: Graphing a Function
Let's say we have the following function:
f(x) = x2- 4x + 3
We could graph this function by plotting points and then connecting the dots, but that would be a lot of work. Instead, we can use a function table to help us out.
First, we'll need to choose a range of input values. For this example, we'll use -2,-1,0,1,and 2. Then, we'll calculate the output for each input value and list the results in a table:
| Input (x) | Output (f(x)) |
| -2 | 15 |
| -1 | 8 |
| 0 | 3 |
| 1 | 0 |
| 2 | -1 |
Now that we have our function table graphing the function is a breeze. We can plot the points from the table and connect the dots. As you can see, using a function table is a much easier way to graph a function than plotting points by hand.
Example 2: Doing Quick Calculations
Function tables don't just make graphing functions easier; they can also be used for quick calculations. Let's say we want to find the value of f(1), where f(x) = x<sup>2</sup>+ 2x - 5. We could plug in 1 for x and calculate the answer by hand, which would be time-consuming. Instead, we can use a function table:
| Input (x) | Output (f(x)) |
| -2 | -5 |
| -1 | -6 |
| 0 | -5 |
| 1 | -2 |
| 2 | 3 |
From the table, we can see that the output for x = 1 is -2. So f(1)= -2. Easy!
Wrapping Up
Function tables are a valuable tool for anyone working with functions, whether they're graphing a function, doing calculations, or just trying to understand how a function behaves. If you ever need to work with a function, make sure to create a function table; it will make your life much easier!