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.

1. Foundations & Basics
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 functions as Processing Machines.
Mapping Diagrams: Domains, ranges, and input-output mappings.
The Vertical Line Test: Testing graphs for function behavior.
Notation & Evaluation:
Function Notation: Understanding f(x), inputs, and algebraic rules.
Evaluating Functions: Solving for f(a) when given an algebraic rule.
Solve Linear Functions: Solving for x when given f(x) = c.

2. Core Linear Functions
Core Concepts:
Distinguishing between Linear and Non-Linear Functions
Finding Slope & Intercepts:
Find Slope (m) and y-intercept (b) from graphs
Find Slope (m) and y-intercept (b) from tables
Slope between Two Points: Find the slope between two points on the line.
Identify Intercepts: Find x- and y-intercepts in standard form.
Writing Linear Functions
Slope & Intercept: Identify parameters from functions.
Find Equation of a Line (from a graph)
Graph the Linear Equation (given the equation)
Function Builder (from a table of values)
Write Equation given Point & Slope
Write Equation given Two-Points
Applications & Relationships
Linear Function Applications: Solving Linear Function word problems.
Parallel & Perpendicular Lines: Determining the relationship between two lines based on their slopes.

3. Families of Functions (Parent Functions)
Overview & Classification:
Introduce the “shapes” of different types of functions.
Parent Functions Introducing standard function shapes.
Classify Functions Linear, Quadratic, Exponential.
Specific Function Families:
Solve Quadratic Functions
Solve Radical Functions
Graphing Quadratic Functions
Graphing Radical Functions
Absolute Value Functions Graph (y = a|x - h| + k)
Absolute Value to Piecewise Functions
Exponential Functions:
Exponential Growth and Decay Models
Graph Exponential Functions
Exponential Function Word Problems
Linear vs. Exponential Growth
Logarithm Functions
Logarithmic Functions & Graphing Game
Piecewise Functions Functions defined by multiple sub-rules across different intervals.

4. Function Transformations
Function Transformations: Shifting, stretching, compressing, and reflecting y = f(x).

5. Advanced Function Analysis & Characteristics
Domain & Range:
Domain of a Function Algebraic constraints for rational and radical functions.
Domain & Range of a Function
Graphical Behaviors & Symmetry:
Increasing/Decreasing Intervals Identifying where graphs rise, fall or constant.
End Behavior Determining what happens to f(x) as x approaches positive or negative infinity.
Extrema (Maximums and Minimums) Identifying local (relative) and absolute peaks and valleys on a graph.
Even and Odd Functions (Symmetry) Testing for algebraic and graphical symmetry.

6. Function Operations & Composition
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 (nested functions)
Composite Functions (Evaluate) (given input values)
Composite Functions (not given input values)

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

8. Systems of Linear Equations
Simultaneous Linear Equations:
Solve Systems of Equations (by substitution)
Solve Systems of Equations (by elimination)

9. Calculus: Function Derivatives & Integrals
Calculus Games

Function Games

Function Table

Write a rule for a function table.

All About Functions

Jeopardy Game

Function Machine

Investigate the relationship between input and output values in a function

Function Game

Advanced game. Rules can use mathematical concepts, including: squares, powers, bases, factors, divisors, modulo, prime numbers, and piecewise functions.

Check out our most popular games!
Fraction Concoction	Fact Family Game	Number Bond Garden
Online Addition Subtraction Game	Penguin Solitaire	Sawayama Solitaire
Ark Solitaire	Eldritch Invasion	Shenzhen Solitaire

Check out more Solitaire games here.

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