Classify Function Game

Classify Function Game
In this game, your goal is to identify the mathematical relationship between the x and y values in a given table. Scroll down for a detailed explanation.
 

 

How to Play the Classify Function Game
Basic Controls
Toggle Mode: Use the switch at the top to move between Normal (Linear vs. Non-Linear) and Hard Mode (Specific categories).
New Table: If you get stuck or want a fresh start, hit the button at the bottom right.
Score: You earn 10 points in Normal mode and 50 points in Hard Mode for every correct identification.

How to Identify the Patterns

1. Linear
   The Look: The y-values increase or decrease by the same amount every time x goes up by 1.
   The Test: Subtract each y value from the next one.
   Example: y = 5, 8, 11, 14. Since 8-5=3, 11-8=3, and 14-11=3, the step is always +3. It’s Linear.
   

2. Quadratic
   The Look: The values grow faster and faster (or slower and slower), but in a predictable way.
   The Test: Subtract the y values to get the “first differences.”
   Then, subtract those results. If that second set of numbers is the same, it’s Quadratic.
   Example: y = 1, 4, 9, 16.
   First differences: 3, 5, 7
   Second differences: 2, 2
   

3. Exponential
   The Look: These values explode or shrink very rapidly.
   The Test: Instead of subtracting, divide a y value by the one before it. If you get the same multiplier every time, it’s Exponential.
   Example: y = 2, 4, 8, 16. Since 4/2=2, 8/4=2, and 16/8=2, the values are doubling.
   

4. None of the Above
   The Look: The numbers look random or don’t follow a smooth curve.
   The Test: If you subtract and get different numbers, and you divide and get different numbers, and the “second difference” isn’t consistent, it’s a “None” pattern.
   

Strategy
In Normal Mode, everything that isn’t a simple addition pattern (Linear) is automatically “Non-Linear.”
In Hard Mode, you must be much more precise. Use a scrap of paper to quickly check the differences between y values.

How to Determine if a Function is Linear, Quadratic, or Exponential from a Table
To determine the type of function from a table, you need to look at how the y-values change as the x-values increase by a constant amount (usually +1). This process is called Finite Difference Analysis.

1. Linear Functions: Constant First Differences
   In a linear function, the y-values change at a constant rate. This means if you subtract each y-value from the one following it, the result will always be the same.
   The Pattern: y₂ - y₁ = y₃ - y₂ = Constant
   The Signal: Addition or subtraction of a fixed number.
   Example: If x goes 1, 2, 3, 4 and y goes 5, 8, 11, 14:
   8 - 5 = 3
   11 - 8 = 3
   14 - 11 = 3
   Result: Linear (Rate of change is 3).
   

2. Quadratic Functions: Constant Second Differences
   Quadratic functions do not have a constant rate of change. Instead, the rate at which the rate changes is constant. You have to perform subtraction twice. The Pattern: Subtract the y-values (First Differences), then subtract those results (Second Differences).
   The Signal: The “steps” grow or shrink by a fixed amount.
   Example: If y goes 1, 4, 9, 16:
   First Differences: 4-1=3, 9-4=5, 16-9=7. (Not linear).
   Second Differences: 5-3=2, 7-5=2.
   Result: Quadratic (The second difference is 2).
   

3. Exponential Functions: Constant Ratios
   Exponential functions grow or decay through multiplication rather than addition. Instead of subtracting, you should divide.
   The Pattern: \(\frac{y_2}{y_1} = \frac{y_3}{y_2} = \text{Constant}\)
   The Signal: Multiplication or division by a fixed number.
   Example: If y goes 2, 6, 18, 54:
   6 / 2 = 3
   18 / 6 = 3
   54 / 18 = 3
   Result: Exponential (Common ratio is 3).
   

This video gives a clear, step-by-step approach to classify of a function.

• Show Video

 

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