This section of our PERT Study Guide defines, categorizes, and reviews how to evaluate functions. Use the breakdown below to review this crucial math concept and take the brief quiz that follows to test your understanding.
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 (“∪” and “∩” shapes).
Exponential functions:
$f(x) = a b^x$
Exponential functions show rapid growth or decay and graph as steep curves. In their equations, the variable occurs in the exponent.
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.