Understanding the Function y = f(x)

A mathematical function is like a machine. You provide an Input (x), it applies a rule or formula f(x), and produces exactly one Output (y).

Input x ➔ Rule f(x) ➔ Output y
Input Panel (x) Velocity Volume
x = 10 m/s
x = 50 L
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Mass (m) is constant at 2 kg
Temperature & Gas Amount are constant
Output Panel (y)
Kinetic Energy Formula: y = ½ m x²
(Since m = 2, rule simplifies to: f(x) = x²)
y = 100 J
Kinetic Energy
Boyle's Law Formula: P × V = k
(Since k = 1000, rule is: f(x) = 1000 / x)
y = 20.0 atm
Pressure

Function Graph: y = f(x)