Math Lesson 6:
Functions

Understanding Functions

A function is a relationship where every input ($x$) from the domain has exactly one output ($y$) in the range. Think of it as a mathematical machine.

Function Notation: We write functions as $f(x)$, where $f$ is the name and $x$ is the input. For example, if $f(x) = 2x$, then $f(5) = 10$.

Linear Functions

A linear function creates a straight line. The standard form is: f(x) = mx + c, where $m$ is the gradient and $c$ is the y-intercept.

Quadratic Functions

Quadratic functions create a U-shaped curve called a parabola. The general form is: f(x) = ax² + bx + c.

Exponential Functions

In an exponential function, the variable is in the exponent: f(x) = a · bˣ. These functions represent rapid growth or decay.

Inverse & Logarithmic Functions

An inverse function, $f^{-1}(x)$, reverses the effect of the original function. The inverse of an exponential function is a logarithmic function.

Example: if $2³ = 8$, then $\log_{2}(8) = 3$.

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