Functions describe relationships between inputs and outputs. A function assigns exactly one output to each input. It is like a rule or machine that takes an input and produces a corresponding output.
Example: The rule "double the input" is a function. Input 3 → output 6. Input 5 → output 10.
Linear functions create straight-line graphs with constant rate of change.
Nonlinear functions have curved graphs with changing rates of change.
Linear example: y = 2x + 3
Nonlinear example: y = x²
Graphs visually represent functions with input on the x-axis and output on the y-axis. Linear functions produce straight lines; nonlinear functions produce curves.
Example: y = 2x + 3 → straight line; y = x² → parabola.
Function to convert Celsius to Fahrenheit: F = (C * 9/5) + 32
Example: 20°C → F = (20 * 9/5) + 32 = 68°F
This is a linear function: constant rate of change (9/5) and fixed starting point (32).
Balance of a savings account over time: B = 100 * (1 + 0.05)^t
Example: After 1 year: B = 100 * 1.05 = 105; after 2 years: B = 100 * (1.05)^2 = 110.25
This is a nonlinear function: exponential growth due to interest compounding; graph is curved with increasing rate of change.