Definition of a Function
A function describes a unique relationship between an input and an output. Each input corresponds to one output, denoted $f(x)$.
Types of Functions
Linear functions:
$f(x) = mx + b$
Linear functions have a constant rate and graph as lines.
Quadratic functions:
$f(x) = ax^2 + bx + c$
Quadratic functions graph as parabolas.
Exponential functions:
$f(x) = a \cdot b^x$
Exponential functions show rapid growth or decay.
Evaluating Functions:
Substitute values into $f(x)$ to find outputs. Example:
If $f(x) = 3x + 2$, then what is $f(2)$?
$f(2) = 3(2) + 2 = 8$
Key Tip: Remember that $f(x)$ doesn’t mean $f × x$. It represents the output of the function when $x$ is the input.