Function Builder Game

Function Builder Game
Your goal in this game is to look at a table of data and figure out the linear rule (the equation) that created those numbers. All linear functions follow the slope-intercept form: f(x) = mx + b. Scroll down for a detailed explanation.
 

 

How to Play the Function Builder Game

1. Choose Your Difficulty
   Standard Mode: The “entry-level” challenge. The table always starts at x = 0 and increases by 1 each time.
   Hard Mode: The “expert” level. The table starts at a random x value, and the x values skip numbers (steps of 2, 3, or 4).
   

2. How to Solve
   Step A: Find the Slope (m)
   The slope is the Rate of Change. It tells you how much f(x) changes for every 1 unit x increases.
   In Standard: Just subtract one f(x) value from the next. If x goes from 1 to 2, and f(x) goes from 5 to 8, your slope is 3.
   In Hard: You must divide. If x goes from 2 to 4 (a change of 2) and f(x) goes from 10 to 20 (a change of 10), your slope is 10 / 2 = 5.
   

Step B: Find the y-Intercept (b)
The intercept is the Starting Value (where x = 0).
In Standard: Just look at the row where x = 0. The f(x) value right there is your b.
In Hard: Since x = 0 is hidden, pick a point you know and “reverse” the slope.
If f(2) = 10 and the slope is 3, go back two steps: 10 - (3 × 2) = 4. So, b = 4.
Or you can use the Algebra Way, which is explained below.

3. Identify the Trap
   The game will try to trick you with “Distractors”:
   The Sign Swap: It might show f(x) = 2x - 5 when the answer is actually 2x + 5.
   The Role Swap: It might swap m and b (e.g., 5x + 2).
   The Delta Trap (Hard Mode Only): It will offer a slope that is just the change in y, hoping you forgot to divide by the change in x.
   

4. Answer
   Click the equation that matches your calculations. If you’re right, it turns emerald. If you’re wrong, the container will shake and reveal the correct answer in green so you can learn for the next round.
   

How to write a linear function from a table?
Writing a linear function from a table is a three-step process. Every linear function can be written in the Slope-Intercept Form:
f(x)=mx+b
m is the slope (the rate of change).
b is the y-intercept (the starting value where x=0).

Step 1: Find the Slope (m)
The slope tells you how much the y value (or f(x)) changes for every 1 unit change in x. To find it, pick any two rows from your table and use the slope formula:
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Example:

x	f(x)
2	7
5	13

Change in y: 13 - 7 = 6
Change in x: 5 - 2 = 3
m = 6 / 3 = 2

Step 2: Find the y-intercept (b)
The y-intercept is the value of f(x) when x = 0.
The Easy Way: Look at your table. If you see a row where x = 0, the y value next to it is your b.
The Algebra Way:
If x=0 isn’t in the table, pick any point (x, y) and plug it into the equation y = mx + b along with the slope you just found.
Example (using m = 2 and the point (2, 7)):
7 = 2(2) + b
7 = 4 + b
3 = b

Step 3: Write the Final Equation
Now, simply replace m and b in the original formula with the numbers you calculated.
Example Final Result:
f(x) = 2x + 3

Quick Check Strategies
Pattern Recognition: If x increases by 1 in every row, the amount f(x) changes by is automatically your slope.
Verification: Pick a row you haven’t used yet (like x=5 from our example) and plug it into your new equation. If 2(5) + 3 equals 13, your equation is correct.

This video gives a clear, step-by-step approach to write a linear function given a table.

• 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.

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