Function Games

Function Games
To build a comprehensive series of online games/worksheets for Functions, we structure the curriculum to move from visual identification to abstract algebraic manipulation.

Relations and Functions

Foundations: What is a Function?
In mathematics, a function is a specific type of relationship between two sets of numbers. It is a rule that takes an input and produces exactly one output. We can look at how functions work using three different perspectives.

The Input-Output Machine: Visualize a function as a “Processing Machine.” You drop a value (x) into the machine. Inside the machine, the rule (f) happens and the output f(x) which is a single, transformed value that pops out.

Mapping Diagrams: The Domain is the set of all possible values you are allowed to put into the function (the x values). The Range is the set of all possible values that can come out of the function (the y values). In a function, one input cannot map to two different outputs.

The Vertical Line Test: You can tell if a graph represents a function by using the Vertical Line Test.

Function Notation
When you see f(x) = 2x + 3, it is read as “f of x equals 2x plus 3."
f: The name of the function.
x: The input (the placeholder).
2x + 3: The rule or “recipe” to follow.

Linear Functions
Slope-Intercept Form: Mastering f(x) = mx + b.
Slope & Intercept: Identify the slope and the y-intercept from the given function.

Write the Linear Function: Given a line write the linear function.

Function Builder: Identify the linear function given a table of values.

Function Evaluation
Evaluating Functions: Solving for f(a) when given an algebraic rule.

Families of Functions (Parent Functions)
Introduce the “shapes” of different types of functions.
Parent Functions

Transformations
How the graph of a parent function, y = f(x), is shifted, stretched, compressed, or reflected based on specific changes to its equation. Function Transformations

Function Operations
Arithmetic of Functions.
Add & Subtract Functions (Evaluate) (given input values)
Add & Subtract Functions (not given input values)

Multiply Functions (Evaluate) (given input values)
Multiply Functions (not given input values)

Divide Functions (Evaluate) (given input values)
Divide Functions (not given input values)

Composition of Functions: The “nested” function concept, f(g(x)).
Composite Functions (Evaluate) (given input values)
Composite Functions (not given input values)

Advanced Characteristics
Domains of Functions (Include Rational & Radical Functions)
Domain of a Function

Inverses: Solving for f^-1(x) and understanding that it reflects across the line y = x.
Inverse of a Function

Piecewise Functions: Functions that have different rules for different intervals.
Increasing/Decreasing Intervals: Identifying where the graph is “climbing” or “falling."

Function Derivatives & Integrals
Calculus Games

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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