Function Machine Game

Function Machine Game
In this Function Machine Game, you are to calculate the correct output based on the given input. Scroll down for a detailed explanation.
 

 

How to Play the Function Machine Game

1. Choose Your Difficulty Mode
   At the very top of the screen, you will see three buttons. Click one to set your challenge level:
   Mode 1: Basic Math:
   The machine uses simple addition and subtraction rules (like f(x) = x + 5).
   Mode 2: Multi-Step:
   The machine uses slightly harder rules involving multiplication, combinations, and even squaring numbers (like f(x) = 2x + 1 or f(x) = x² + 2).
   Mode 3: Work Backwards:
   The machine will give you the final output and the rule, and you have to figure out what number was originally dropped into the top.
   

2. Check the Rule and the Variables
   Once you select a mode, look at the center of the blue machine. The yellow text is your function rule for this round.
   If you are in Mode 1 or 2:
   Look at the top funnel or the text below the machine to find your Input (x). Substitute that number into the rule to calculate your answer.
   If you are in Mode 3:
   Look at the bottom pipe or the text below the machine to find your Output f(x). You will see a ? at the top. You need to use algebra to reverse the rule and find the starting input.
   

3. Process Your Answer
   Once you have calculated the missing number (either the output or the input, depending on your mode), type it into the text box at the bottom.
   Click PROCESS (or press the Enter key on your keyboard).
   

4. Score Points
   Correct: The text will turn green, the correct number will appear in the machine, and your score will go up by 1.
   Incorrect: The text will turn red and reveal what the correct number should have been, helping you learn from the mistake.
   Click the NEXT PROBLEM → button to load a fresh puzzle and keep building your score.
   

What is a function?
In mathematics, a function is a specific type of relationship between two sets of numbers. You can think of it as a rule that takes an input and produces exactly one output.
Here is a breakdown of how functions work using three different perspectives.

1. The Machine Metaphor
   The easiest way to visualize a function is as a “Processing Machine."
   The Input (x):
   You drop a value into the top of the machine.
   The Rule (f):
   Inside the machine, a specific mathematical operation happens (like “add 5” or “multiply by 2”).
   The Output (f(x)):
   A single, transformed value pops out the bottom.
   The golden rule of functions is consistency: if you put the same number into the machine twice, you must get the same result both times.
   

2. Inputs and Outputs (Domain and Range)
   To talk about functions like a mathematician, you need to know these three terms:
   Domain:
   The set of all possible values you are allowed to put into the function (the x values).
   Range:
   The set of all possible values that can come out of the function (the y values).
   Mapping:
   The process of connecting one input to one output. In a true function, one input cannot map to two different outputs.
   

3. The Vertical Line Test (Graphs)
   When you plot a function on a graph, it creates a visual “path.” You can tell if a graph represents a function by using the Vertical Line Test. If you can draw a vertical line anywhere on the graph and it only touches the curve once, it is a function. If the line touches the curve twice (or more), it means one x value has multiple y values, which breaks the rule of a function.
   

This video gives a clear, step-by-step approach to understand function machines.

• Show Video

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.