Function Machines
Input-Output Activity to Understand Types of Functions
Explore different types of mathematical functions by entering inputs and observing the outputs. Change the function type to see how the relationship between input and output changes!
5
→
x + 3
→
8
Observation:
Linear functions change by constant amounts. For f(x) = x + 3, each increase of 1 in x increases the output by 1.
The Mathematics Behind Functions
Key Concepts:
Functions are relationships where each input has exactly one output:
- Linear: f(x) = mx + b (constant rate of change)
- Quadratic: f(x) = ax² + bx + c (U-shaped parabola)
- Exponential: f(x) = aˣ (rapid growth or decay)
Real-world Applications:
Functions model many real-world phenomena - linear for constant speed, quadratic for projectile motion, exponential for population growth or radioactive decay.
